Question

Решите уравнения:tgx в квадрате -1=0

Answer 1

$tg^2x-1=0\\tg^2x=1\\tgx=\pm1\\x=\pm \frac{\pi}{4}+\pi n, \; n\in Z.$
Или так:
$tg^2x-1=0\\(tgx-1)(tgx+1)=0\\\\tgx-1=0\\tgx=1\\x=\frac{\pi}{4}+\pi n, \; n\in Z;\\\\ tgx+1=0\\tgx=-1\\x=-\frac{\pi}{4}+\pi n, \; n\in Z.$