What is the General Solution of $tan^2 \theta$ =$tan^2 \alpha$ ?

Solution :

The general solution of $tan^2 \theta$ = $tan^2 \alpha$ is given by $\theta$ = $n\pi \pm \alpha$, n $\in$ Z.

Proof :

We have, $tan^2 \theta$ =$tan^2 \alpha$

$\implies$  $1 – tan^2\theta\over 1 + tan^2 \theta$ =$1 – tan^2\alpha\over 1 + tan^2 \alpha$

$\implies$   $cos 2\theta$ = $cos 2\alpha$

$\implies$  $2\theta$ = $2n\pi \pm 2\alpha$,  n $\in$  Z.

$\implies$  $\theta$ = $n\pi \pm \alpha$, n $\in$ Z.