A) \[1/2\]
B) \[\pi /4\]
C) 0
D) 1
Correct Answer: D
Solution :
\[y={{\tan }^{-1}}\left[ \frac{\sin x+\cos x}{\cos x-\sin x} \right]\]\[={{\tan }^{-1}}\left[ \frac{1+\tan x}{1-\tan x} \right]\] \[={{\tan }^{-1}}\left[ \frac{\tan (\pi /4)+\tan x}{1-\tan (\pi /4)\tan x} \right]\]\[={{\tan }^{-1}}\tan (\pi /4+x)\] Þ \[y=(\pi /4)+x\]Þ \[dy/dx=1\].You need to login to perform this action.
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