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Question: \[\int_{}^{}{\frac{1 - \tan x}{1 + \tan x}\mspace{6mu} dx =}\]...

∫1−tan⁡x1+tan⁡x 6mudx=\int_{}^{}{\frac{1 - \tan x}{1 + \tan x}\mspace{6mu} dx =}

A

logsec(π4−x)+c{logsec}\left( \frac{\pi}{4} - x \right) + c

B

logcos(π4+x)+c{logcos}\left( \frac{\pi}{4} + x \right) + c

C

logsin(π4+x)+c{logsin}\left( \frac{\pi}{4} + x \right) + c

D

None of these

Answer

logcos(π4+x)+c{logcos}\left( \frac{\pi}{4} + x \right) + c

Explanation

Solution

log⁡(1+cot⁡x)+c\log(1 + \cot x) + c