Question
Mathematics Question on Trigonometric Identities
If cot(sin−1x)=cos(tan−13) , then x=
A
0
B
32
C
2
D
52
Answer
52
Explanation
Solution
We have, cot(sin−1x)
=cos(tan−13)
⇒cot(sin−1x)=cos(3π)=21
⇒sin−1x=cot−1(21)
⇒x=sin[cot−1(21)]
=sin[sin−1(52)]
∴x=52
[∵cot−1(21)=θ⇒cotθ=21∴sinθ=52]