Inverse Trigonometric Functions Question 140
Question: The function $ f(x)={{\tan }^{-1}}(\sin x+\cos x) $ is an increasing function in
Options:
A) $ ( \frac{\pi }{4},\frac{\pi }{2} ) $
B) $ ( -\frac{\pi }{2},\frac{\pi }{4} ) $
C) $ ( 0,\frac{\pi }{2} ) $
D) $ ( -\frac{\pi }{2},\frac{\pi }{2} ) $
Show Answer
Answer:
Correct Answer: B
$ f’(x)=\frac{1}{1+{{(\sin x+\cos x)}^{2}}}(\cos x-\sin x) $
$ f(x) $ is increasing if $ \cos x-\sin x>0 $
Or $ \cos x>\sin x $ Hence, $ f(x) $ is increasing when $ x\in ( -\frac{\pi }{2},\frac{\pi }{4} ) $
BETA
