Differentiation Question 364
Question: $ \frac{d}{dx}( {{\tan }^{-1}}\sqrt{\frac{1+\cos \frac{x}{2}}{1-\cos \frac{x}{2}}} ) $ is equal to
[MP PET 2004]
Options:
A) $ -\frac{1}{4} $
B) $ \frac{1}{2} $
C) $ -\frac{1}{2} $
D) $ \frac{1}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y={{\tan }^{-1}}\sqrt{\frac{1+\cos \frac{x}{2}}{1-\cos \frac{x}{2}}}={{\tan }^{-1}}\sqrt{\frac{2{{\cos }^{2}}\frac{x}{4}}{2{{\sin }^{2}}\frac{x}{4}}} $
$ y={{\tan }^{-1}}\cot \frac{x}{4}={{\tan }^{-1}}\tan ( \frac{\pi }{2}-\frac{x}{4} )=\frac{\pi }{2}-\frac{x}{4} $
\ $ \frac{dy}{dx}=-\frac{1}{4} $ .
BETA
