Question

Write the general solutions of tan² 2x = 1.

Answer 1

Given:

$$\begin{gathered} {\tan }^{2}2x=1 \\ \Rightarrow \tan 2x=\tan \frac{\mathrm{\pi }}{4} \\ \Rightarrow 2x=n\mathrm{\pi }+\frac{\mathrm{\pi }}{4} \\ \Rightarrow x\mathit{}=\frac{n\pi }{2}+\frac{\mathrm{\pi }}{8},n\in Z \end{gathered}$$

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