Question

решите тригонометрическое неравенство:
tg(2x+2п/3)≤√3/3

Answer 1

$tg(2x+\frac{2\pi}{3})\leq \frac{\sqrt{3}}{3}\\\\-\frac{\pi}{2}+\pi n<2x+\frac{2\pi}{3}\leq\frac{\pi}{6}+\pi n\\\\-\frac{\pi}{2}-\frac{2\pi}{3}+\pi n<2x\leq\frac{\pi}{6}-\frac{2\pi}{3} +\pi n\\\\-\frac{7\pi}{6}+\pi n<2x\leq -\frac{\pi}{2} +\pi n\\\\-\frac{7\pi}{12}+\frac{\pi n}{2}<x\leq -\frac{\pi}{4} +\frac{\pi n}{2}$

x ∈ $(-\frac{7\pi}{12}+\frac{\pi n}{2} ;-\frac{\pi}{4}+\frac{\pi n}{2}]$

Answer 2

Решение (см. изображение)