Question

Решите неравенство tg(3x-pi/4)≥√3

Answer 1

$tg(3x -\frac{\pi}{4}) \geq \sqrt{3} \\ tg(3x -\frac{\pi}{4}) \geq arctg \sqrt{3}+\pi n \\ 3x- \frac{\pi}{4} \geq arctg \sqrt{3}+\pi n \\ 3x \geq \frac{\pi}{4} +arctg \sqrt{3}+\pi n \\ x \geq \frac{\pi}{12}+arctg \frac{ \sqrt{3} }{3}+ \frac{\pi n}{3} ,n\in Z$