Подробное задание во вложении

0" alt="1-cos\frac{x}{2}>0" align="absmiddle" class="latex-formula">

$2cos\frac{x}{2}<1$

$cos\frac{x}{2}<\frac{1}{2}$

$\frac{\pi}{3}+2\pi*k<\frac{x}{2}<\frac{5\pi}{3}+2\pi*k$

$\frac{2\pi}{3}+4\pi*k<x<\frac{10\pi}{3}+4\pi*k$

$tg(\pi-x)<0$

$-tgx<0|*(-1)$

0" alt="tgx>0" align="absmiddle" class="latex-formula">

$2\pi*n<x<\frac{\pi}{2}+\pi*n$

$2cos(x+\frac{\pi}{3})-\sqrt{3}<0$

$cos(x+\frac{\pi}{3})<\frac{\sqrt{3}}{2}$

$\frac{\pi}{6}+2\pi*k<x+\frac{\pi}{3}<\frac{11\pi}{6}+2\pi*k$

$\frac{\pi}{2}+2\pi*k<x<\frac{13\pi}{6}+2\pi*k$