xsin³A+ycos³A=sinA.cosA and xsinA=ycosA Prove that x²+y²=1
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Suman Chimpa 6 years, 4 months ago
- 1 answers
Test
Related Questions
Posted by Lakshay Kumar 1 year, 1 month ago
- 0 answers
Posted by Parinith Gowda Ms 3 months, 3 weeks ago
- 1 answers
Posted by Vanshika Bhatnagar 1 year, 4 months ago
- 2 answers
Posted by Hari Anand 6 months, 1 week ago
- 0 answers
Posted by Kanika . 1 month, 1 week ago
- 1 answers
Posted by Parinith Gowda Ms 3 months, 3 weeks ago
- 0 answers
Posted by Sahil Sahil 1 year, 4 months ago
- 2 answers
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
Sia ? 6 years, 4 months ago
We have,
xsin3{tex}\theta{/tex} + ycos3{tex}\theta{/tex} = sin{tex}\theta{/tex} cos{tex}\theta{/tex}
{tex}\Rightarrow{/tex} (xsin{tex}\theta{/tex}) sin2{tex}\theta{/tex} + (ycos{tex}\theta{/tex}) cos2{tex}\theta{/tex} = sin{tex}\theta{/tex} cos{tex}\theta{/tex}
{tex}\Rightarrow{/tex} x sin{tex}\theta{/tex} (sin2{tex}\theta{/tex}) + (x sin{tex}\theta{/tex}) cos2{tex}\theta{/tex} = sin{tex}\theta{/tex} cos{tex}\theta{/tex} [{tex}\because{/tex} x sin{tex}\theta{/tex} = y cos{tex}\theta{/tex}]
{tex}\Rightarrow{/tex} x sin{tex}\theta{/tex} (sin2{tex}\theta{/tex} + cos2{tex}\theta{/tex}) = sin{tex}\theta{/tex} cos{tex}\theta{/tex}
{tex}\Rightarrow{/tex} x sin{tex}\theta{/tex} = sin{tex}\theta{/tex} cos{tex}\theta{/tex}
{tex}\Rightarrow{/tex} x = cos{tex}\theta{/tex}
Now, xsin {tex}\theta{/tex} = ycos{tex}\theta{/tex}
{tex}\Rightarrow{/tex} cos{tex}\theta{/tex} sin{tex}\theta{/tex} = y cos{tex}\theta{/tex} [{tex}\because{/tex} x = cos{tex}\theta{/tex}]
{tex}\Rightarrow{/tex} y = sin{tex}\theta{/tex}
Hence, x2 + y2 = cos2{tex}\theta{/tex} + sin2{tex}\theta{/tex} = 1
1Thank You