Question

Solve:

tan $(\pi -ta{n}^{-1}z)$ = z.

Answer 1

$\tan (\pi -{\tan }^{-1}(z\left)\right)=z$

$-\tan \left({\tan }^{-1}z\right)=z$ $\left[\tan \right(\pi -\alpha )=-\tan \alpha ,\tan ({\tan }^{-1}\left(\theta \right))=\theta ]$

$\Rightarrow -z=z$

$\Rightarrow 2z=0$

$\Rightarrow z=0$.