Question

${\tan }^{-1}\frac{\cos x-\sin x}{\cos x+\sin x},\frac{-\pi }{4}<x<\frac{3\pi }{4}$

Answer 1

Divide each term of numerator inside the brackets by $\cos x$
${\tan }^{-1}\left[\tan (\frac{\pi }{4}-x)\right][\because \frac{1-\tan x}{1+\tan x}=\tan (\frac{\pi }{4}-x)]$
$\Rightarrow \frac{\pi }{4}-x$