Differentiation Question 300
Question: If $ y={{\tan }^{-1}}[ \frac{\sin x+\cos x}{\cos x-\sin x} ], $ then $ \frac{dy}{dx} $ is
[UPSEAT 2001]
Options:
A) $ 1/2 $
B) $ \pi /4 $
C) 0
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
$ y={{\tan }^{-1}}[ \frac{\sin x+\cos x}{\cos x-\sin x} ] $
$ ={{\tan }^{-1}}[ \frac{1+\tan x}{1-\tan x} ] $
$ ={{\tan }^{-1}}[ \frac{\tan (\pi /4)+\tan x}{1-\tan (\pi /4)\tan x} ] $
$ ={{\tan }^{-1}}\tan (\pi /4+x) $
Therefore $ y=(\pi /4)+x $
Therefore $ dy/dx=1 $ .
BETA
