Question

Решите неравенство: tg x/3 больше либо равно tg П/6

Answer 1

$tg\frac{x}{3}\geq tg\frac{\pi}{6}\\\\arctg(tg\frac{\pi}{6})+\pi n\leq \frac{x}{3}<\frac{\pi}{2}+\pi n\; ,\; n\in Z\\\\\frac{\pi}{6}+\pi n\leq \frac{x}{3}\leq \frac{\pi}{2}+\pi n\; ,\; n\in Z\\\\\frac{\pi}{2}+3\pi n\leq x<\frac{3\pi}{2}+3\pi n\; ,\; n\in Z\\\\x\in [\, \frac{\pi}{2}+3\pi n\, ,\, \frac{3\pi }{3}+3\pi n\, )\; ,\; n\in Z$