Write the general solutions of tan
Question:

Write the general solutions of tan2 2x = 1.

Solution:

Given:

$\tan ^{2} 2 x=1$

$\Rightarrow \tan 2 x=\tan \frac{\pi}{4}$

$\Rightarrow 2 x=n \pi+\frac{\pi}{4}$

$\Rightarrow x=\frac{n \pi}{2}+\frac{\pi}{8}, n \in Z$

Hence, the general solution of the equation is $\frac{n \pi}{2}+\frac{\pi}{8}, n \in Z$.