Differentiation Question 244
Question: If $ f(x)={{\tan }^{-1}}( \frac{\sin x}{1+\cos x} ) $ ,then $ f’( \frac{\pi }{3} )= $
[BIT Ranchi 1990]
Options:
A) $ \frac{1}{2(1+\cos x)} $
B) $ \frac{1}{2} $
C) $ \frac{1}{4} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)={{\tan }^{-1}}( \frac{\sin x}{1+\cos x} )={{\tan }^{-1}}[ \tan \frac{x}{2} ]=\frac{x}{2} $
Therefore $ f’(x)=\frac{1}{2}. $ Hence $ f’( \frac{\pi }{3} )=\frac{1}{2} $ .
BETA
