Question

Решить уравнение 2tg(pi/4 - x/2) = -1

Answer 1

$2tg(\frac{\pi}{4}-\frac{x}{2})=-1\\\\tg(\frac{\pi}{4}-\frac{x}{2})=-\frac{1}{2}\\\\\frac{\pi}{4}-\frac{x}{2}=-arctg\frac{1}{2}+\pi n\; ,\; n\in Z\\\\\frac{x}{2}=\frac{\pi}{4}+arctg\frac{1}{2}-\pi n\; ,\; n\in Z\\\\x=\frac{\pi}{2}+2arctg\frac{1}{2}-2\pi n\; ,\; n\in Z$