عبارت $Cotx(4\operatorname{Sin}x+\tan x)$ را ساده می‌کنیم: $Cotx(4\operatorname{Sin}x+\tan x)=4\operatorname{Sin}xCotx+\underbrace{Cotx.\tan x=}_{1}4\operatorname{Sin}x\times \frac{\operatorname{Cos}x}{\operatorname{Sin}x}+1$ $=4\operatorname{Cos}x+1\Rightarrow 2\operatorname{Cos}2x=4\operatorname{Cos}x+1\Rightarrow 2(2{{\operatorname{Cos}}^{2}}x-1)$ $=4\operatorname{Cos}x+1\Rightarrow 4{{\operatorname{Cos}}^{2}}x-4\operatorname{Cos}x-3=0\xrightarrow{\operatorname{Cos}x=A}4{{A}^{2}}-4A-3=0,\Delta =64$  $A=\frac{4\pm 8}{8}\Rightarrow \left\{ _{A=-\frac{1}{2}=\operatorname{Cos}x\Rightarrow x=2k\pi \pm \frac{2\pi }{3}}^{A=\frac{3}{2}\rangle 1} \right.$