Question

Evaluate:

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

Answer 1

$Ta{n}^{-1}\left(\frac{cosx+sinx}{cosx-sinx}\right)$

$Ta{n}^{-1}\left(\frac{cosx(1+Tanx)}{cosx(1-Tanx)}\right)$

$Ta{n}^{-1}\left(\frac{1+Tanx}{1-Tanx}\right)$

$Ta{n}^{-1}\left(Tan(\frac{\pi }{4}+x)\right)$

$=\frac{\pi }{4}+x$