Question

3tan^2 (2x)$\leq$1

Answer 1

$3tg^22x\leq 1\\\\tg^22x\leq \frac{1}{3}\\\\tg^22x-\frac{1}{3}\leq 0\; \; \to \; \; \; (tg2x-\frac{1}{\sqrt3})(tg2x+\frac{1}{\sqrt3})\leq 0\\\\-\frac{1}{\sqrt3}\leq tg2x\leq \frac{1}{\sqrt3}\\\\-\frac{\pi}{6}+\pi n\leq 2x\leq \frac{\pi}{6}+\pi n\; ,\; n\in Z\\\\-\frac{\pi}{12}+\frac{\pi n}{2}\leq x\leq \frac{\pi}{12}+\frac{\pi n}{2}\; ,\; n\in Z$