Question

Tg^3x=tg x Решить уравнение

Answer 1

$tg^3x=tgx\\ tgx(tg^2x-1)=0\\ \\ \left[\begin{array}{ccc}tgx=0\\ tg^2x=1\end{array}\right\Rightarrow~~~ \left[\begin{array}{ccc}tgx=0\\ tgx=\pm1\end{array}\right\Rightarrow~~~~~ \left[\begin{array}{ccc}x_1= \pi n,n \in \mathbb{Z}\\ x_{2,3}=\pm \frac{\pi}{4}+ \pi n,n \in \mathbb{Z} \end{array}\right$