{"id":4586,"date":"2016-05-17T09:49:00","date_gmt":"2016-05-17T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-3-3\/"},"modified":"2016-05-17T10:40:47","modified_gmt":"2016-05-17T05:10:47","slug":"ncert-solutions-class-11-maths-exercise-3-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-3-3\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 3.3"},"content":{"rendered":"<p style=\"text-align: justify;\"><strong>Exercise 3.3<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Prove that:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>1. L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image004.png\" \/> R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 213px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image010.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 209px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 185px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image016.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 225px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image022.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>5. Find the value of: <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong><img decoding=\"async\" style=\"height: 21px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong><img decoding=\"async\" style=\"height: 21px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 29px; width: 359px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 271px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 281px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 48px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 91px; width: 235px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image030.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>Prove the following:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>6. <\/strong><img decoding=\"async\" style=\"height: 45px; width: 397px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 45px; width: 316px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 257px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 195px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image035.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>7. <\/strong><img decoding=\"async\" style=\"height: 88px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 88px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">[Using <img decoding=\"async\" style=\"height: 44px; width: 349px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image038.png\" \/>]\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 155px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image039.png\" \/> = <img decoding=\"async\" style=\"height: 80px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 56px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image041.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>8. <\/strong><img decoding=\"async\" style=\"height: 68px; width: 203px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 68px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 47px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image044.png\" \/> = <img decoding=\"async\" style=\"height: 44px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image045.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>9. <\/strong><img decoding=\"async\" style=\"height: 48px; width: 372px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 48px; width: 351px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 51px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 1 = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>10. <\/strong><img decoding=\"async\" style=\"height: 27px; width: 365px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 27px; width: 317px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image055.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>11. <\/strong><img decoding=\"async\" style=\"height: 45px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 45px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image058.png\" \/> = <img decoding=\"async\" style=\"height: 45px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image059.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image060.png\" \/> = <img decoding=\"async\" style=\"height: 44px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 23px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image062.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>12. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image064.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 267px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image067.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>13. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image068.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image069.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image070.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image072.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>14. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image073.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 19px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image074.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image075.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 392px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image078.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image081.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>15. <img decoding=\"async\" style=\"height: 27px; width: 294px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image082.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 27px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image084.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image085.png\" \/> = <img decoding=\"async\" style=\"height: 19px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image086.png\" \/><\/p>\n<p style=\"text-align: justify;\">R.H.S. = <img decoding=\"async\" style=\"height: 27px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image087.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image088.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image089.png\" \/> = <img decoding=\"async\" style=\"height: 19px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image086.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image090.png\" \/>L.H.S. = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>16. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image091.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image092.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image093.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image094.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>17. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image097.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image098.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>18. <\/strong><img decoding=\"async\" style=\"height: 45px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image099.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 44px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image100.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image101.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image102.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>19. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image103.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image104.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image105.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image106.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>20. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image107.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image108.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 52px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image109.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 64px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image110.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image111.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>21. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image112.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image113.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image114.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 88px; width: 249px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image115.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image116.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image117.png\" \/> = <img decoding=\"async\" style=\"height: 19px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image118.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>22. <\/strong><img decoding=\"async\" style=\"height: 19px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image119.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that <img decoding=\"async\" style=\"height: 27px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image120.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image121.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image122.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image121.png\" \/><img decoding=\"async\" style=\"height: 27px; width: 245px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image123.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image121.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image124.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image121.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 295px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image125.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image121.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image119.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>23. <\/strong><img decoding=\"async\" style=\"height: 48px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image126.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 41px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image127.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 87px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image128.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 102px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image129.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 52px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image130.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image131.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>24. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image132.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image133.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image134.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image135.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image136.png\" \/> = R.H.S.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>25. <\/strong><img decoding=\"async\" style=\"height: 21px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image137.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong> L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image138.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 32px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image139.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 235px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image140.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image141.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 21px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch03\/Ex3.3\/image142.png\" \/> = R.H.S.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exercise 3.3 Prove that: 1. Ans. 1. L.H.S. = = = R.H.S. 2. Ans. L.H.S. = = = = = 3. Ans. L.H.S. = = = = = = R.H.S. 4. Ans. L.H.S. = = = = = = R.H.S. 5. Find the value of: (i) (ii) Ans. (i) = (ii) = = Prove the &#8230; <a title=\"NCERT Solutions class-11 Maths Exercise 3.3\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-3-3\/\" aria-label=\"More on NCERT Solutions class-11 Maths Exercise 3.3\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4586","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class-11 Maths Exercise 3.3 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-3-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 3.3 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 3.3 Prove that: 1. Ans. 1. L.H.S. = = = R.H.S. 2. Ans. L.H.S. = = = = = 3. Ans. L.H.S. = = = = = = R.H.S. 4. Ans. L.H.S. = = = = = = R.H.S. 5. Find the value of: (i) (ii) Ans. (i) = (ii) = = Prove the ... 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