Question

Решите уравнение:

$3cosfrac{x}{2}-sqrt3sinfrac{x}{2}leqsqrt3$

Answer 1

$3cosfrac{x}{2}-sqrt3sinfrac{x}{2}leqsqrt3\ sqrt3cosfrac{x}{2}-sinfrac{x}{2}leq1|:2\ frac{sqrt3}{2}cosfrac{x}{2}-frac{1}{2}sinfrac{x}{2}leqfrac{1}{2}\ cosfrac{pi}{6}cosfrac{x}{2}-sinfrac{pi}{6}sinfrac{x}{2}leqfrac{1}{2}\ cos(frac{pi}{6}+frac{x}{2})leq frac{1}{2}\ frac{pi}{3}+2pi nleqfrac{pi}{6}+frac{x}{2}leqfrac{5pi}{3}+2pi n\ frac{pi}{6}+2pi nleqfrac{x}{2}leqfrac{9pi}{6}+2pi n\ frac{pi}{3}+4pi nleq x leq 3pi+4pi n$