Ask questions which are clear, concise and easy to understand.
Ask QuestionPosted by Prince M Varghese 6 years, 2 months ago
- 0 answers
Posted by Manisha Tiwari 6 years, 2 months ago
- 2 answers
Posted by Mohit Sharma 6 years, 2 months ago
- 0 answers
Posted by Shivam Maddheshiya 6 years, 2 months ago
- 0 answers
Posted by Aditi Shinde 6 years, 2 months ago
- 0 answers
Posted by Radhey Shyam 5 years, 8 months ago
- 1 answers
Posted by Garima Sharma 6 years, 2 months ago
- 4 answers
Posted by Dalvi Santosh 6 years, 2 months ago
- 0 answers
Posted by Sandeep Dubey 6 years, 2 months ago
- 0 answers
Posted by Gaurav Kumar 6 years, 2 months ago
- 1 answers
Pujitha A 6 years, 2 months ago
Posted by Vansh Verma 6 years, 2 months ago
- 3 answers
Hari Haran 6 years, 2 months ago
Posted by Meet Koriya 6 years, 2 months ago
- 0 answers
Posted by Aparna Sinha 6 years, 2 months ago
- 3 answers
Iram Hasan Hasan 6 years, 2 months ago
Sia ? 6 years, 2 months ago
cos 10 + cos 110 + cos 130 = (cos 10 + cos 110) + cos 130
= {tex}2cos \frac{(110+10)}{2}\times cos\frac{(110-10)}{2}{/tex} + cos 130 {using cos C + cos D}
= {tex}2cos \frac {(C+D)}{2}{/tex}{tex}\times{/tex} {tex}cos\frac {(C-D)}{2}{/tex}
={tex}2cos\frac{120}{2}{/tex} {tex}\times{/tex} {tex}cos\frac {100}{2}{/tex}+ cos (180 - 50) (As 130 = 180 - 50)
= 2 cos 60 {tex}\times{/tex} cos 50 - cos 50 (Using cos (180 - A) = - cos A)
= 2 {tex}\times{/tex}{tex}\frac{1}{2}{/tex}{tex}\times{/tex} cos 50 - cos 50 ( As cos 60 = {tex}\frac{1}{2}{/tex})
= cos 50o - cos 50o = 0
Posted by Vaishnavi Pagare 6 years, 2 months ago
- 4 answers
Posted by Rahul Fernandes 6 years, 2 months ago
- 1 answers
Posted by Kartik Aasht 6 years, 2 months ago
- 1 answers
Posted by Sushant Patil 6 years, 2 months ago
- 1 answers
Sia ? 6 years, 2 months ago
LHS = {tex}\frac { 1 + \sin \theta - \cos \theta } { 1 + \sin \theta + \cos \theta }{/tex}
= {tex}\frac { ( 1 - \cos \theta ) + \sin \theta } { ( 1 + \cos \theta ) + \sin \theta }{/tex} = {tex}\frac { 2 \sin ^ { 2 } \frac { \theta } { 2 } + 2 \sin \frac { \theta } { 2 } \cdot \cos \frac { \theta } { 2 } } { 2 \cos ^ { 2 } \frac { \theta } { 2 } + 2 \sin \frac { \theta } { 2 } \cdot \cos \frac { \theta } { 2 } }{/tex}
[{tex}\because{/tex} sin2x = {tex}\frac { 1 - \cos 2 x } { 2 } \Rightarrow{/tex} {tex}2 sin^2x = 1 - cos 2x{/tex} and {tex}2sin^2 \frac{x}{2} = 1 - cosx{/tex} and {tex}2 cos^2{/tex} {tex}\frac { x } { 2 }{/tex} {tex}= 1 + cosx{/tex} and {tex}sinx = 2sin{/tex} {tex}\frac { x } { 2 }{/tex} {tex}\times{/tex} {tex}cos{/tex} {tex}\frac { x } { 2 }{/tex}]
= {tex}\frac { \sin ^ { 2 } \frac { \theta } { 2 } + \sin \frac { \theta } { 2 } \cdot \cos \frac { \theta } { 2 } } { \cos ^ { 2 } \frac { \theta } { 2 } + \sin \frac { \theta } { 2 } \cdot \cos \frac { \theta } { 2 } } = \frac { \sin \frac { \theta } { 2 } \left[ \sin \frac { \theta } { 2 } + \cos \frac { \theta } { 2 } \right] } { \cos \frac { \theta } { 2 } \left[ \cos \frac { \theta } { 2 } + \sin \frac { \theta } { 2 } \right] }{/tex}
= {tex}\frac { \sin \frac { \theta } { 2 } } { \cos \frac { \theta } { 2 } }{/tex} = tan {tex}\frac { \theta } { 2 }{/tex} = RHS
{tex}\therefore{/tex} LHS = RHS
Hence proved.
Posted by Anurag Kumar 6 years, 2 months ago
- 0 answers
Posted by Utkarsh Singhal 6 years, 2 months ago
- 0 answers
Posted by Sachin Sharma 6 years, 2 months ago
- 1 answers
Sachin Tiwari 6 years, 2 months ago
Posted by Adarsh Pandey 6 years, 2 months ago
- 0 answers
Posted by Uday Sharma 6 years, 2 months ago
- 0 answers
Posted by Simranjeet Kaur 6 years, 2 months ago
- 1 answers
Gaurav Seth 6 years, 2 months ago
Sum of m terms of an A.P. = m/2 [2a + (m -1)d]
Sum of n terms of an A.P. = n/2 [2a + (n -1)d]
m/2 [2a + (m -1)d] / n/2 [2a + (n -1)d] = m:n
⇒ [2a + md - d] / [2a + nd - d] = m/n
⇒ 2an + mnd - nd = 2am + mnd - md
⇒ 2an - 2am = nd - md
⇒ 2a (n -m) = d(n - m)
⇒ 2a = d
Ratio of m th term to nth term:
[a + (m - 1)d] / [a + (n - 1)d]
= [a + (m - 1)2a] / [a + (n - 1)2a]
= a [1 + 2m - 2] / a[1 + 2n -2]
= (2m - 1) / (2n -1)
So, the ratio of mth term and the nth term of the arithmetic series is (2m - 1):(2n -1).
Posted by Sarata Kumar Pradhan 6 years, 2 months ago
- 0 answers
Posted by Pratap Mandal 6 years, 2 months ago
- 2 answers
Abhiraj Singh 6 years, 2 months ago
Posted by Shaktiraj Mallah 6 years, 2 months ago
- 0 answers
Posted by Gurdit Singh 6 years, 2 months ago
- 1 answers
Aditya Narayan Singh 6 years, 2 months ago
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
