# 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.