Question

Решить неравенство tg(x/2) < 1

Answer 1

$tg\frac{x}{2}<1\\\\-\frac{\pi }{2}+\pi n<\frac{x}{2}<arctg1+\pi n,n\in z\\\\-\frac{\pi }{2}+\pi n<\frac{x}{2}<\frac{\pi }{4}+\pi n,n\in z\\\\-\pi+2\pi n<x<\frac{\pi }{2}+2\pi n,n\in z\\\\x\in(-\pi +2\pi n;\frac{\pi }{2}+2\pi n),n\in z$