Differentiation Question 58
Question: If $ y={{\cot }^{-1}}[ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} ] $ , then $ \frac{dy}{dx}= $
Options:
A) $ \frac{1}{2} $
B) $ \frac{2}{3} $
C) 3
D) 1
Show Answer
Answer:
Correct Answer: A
Solution:
$ y={{\cot }^{-1}}[ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} ] $
$ ={{\cot }^{-1}}[ \frac{2+2\cos x}{2\sin x} ]={{\cot }^{-1}}[ \frac{1+\cos x}{\sin x} ] $
$ ={{\cot }^{-1}}[ \cot \frac{x}{2} ]=\frac{x}{2} $
$ \therefore \frac{dy}{dx}=\frac{1}{2} $ .
BETA
