${\tan ^{ - 1}}\left( {\frac{{\cos x - \sin x}}{{\cos x + \sin x}}} \right),\;0 < x < \pi$

${\tan ^{ - 1}}\left( {\frac{{\cos x - \sin x}}{{\cos x + \sin x}}} \right) = {\tan ^{ - 1}}\left( {\frac{{1 - \tan x}}{{1 + \tan x}}} \right)$

(Dividing numerator and denominator by cos x)

$= {\tan ^{ - 1}}\left( {\tan \left( {\frac{\pi }{4} - x} \right)} \right) = \frac{\pi }{4} - x$