Question

Корень из 3 ctg(pi/4-2x)>1

Answer 1

$\sqrt3ctg(\frac{\pi}{4}-2x)\ \textgreater \ 1\\-\sqrt3ctg(\frac{\pi}{4}-2x)\ \textgreater \ 1\\ctg(2x-\frac{\pi}{4})\ \textless \ -\frac{1}{\sqrt3}=-\frac{\sqrt3}{3}\\\frac{2\pi}{3}+\pi n\ \textless \ 2x-\frac{\pi}{4}\ \textless \ \pi+\pi n\\\frac{11\pi}{12}+\pi n\ \textless \ 2x\ \textless \ \frac{5\pi}{4}+\pi n\\\frac{11\pi}{24}+\frac{\pi n}{2}\ \textless \ x\ \textless \ \frac{5\pi}{8}+\frac{\pi n}{4}, \; n \in Z$