سمت چپ معادله را ساده می‌کنیم: $2\tan x.{{\operatorname{Cos}}^{2}}x=2\times \frac{\operatorname{Sin}x}{\operatorname{Cos}x}.{{\operatorname{Cos}}^{2}}x=2\operatorname{Sin}x\operatorname{Cos}x=\operatorname{Sin}2x$ $\Rightarrow \operatorname{Sin}2x=1\Rightarrow 2x=2k\pi +\frac{\pi }{2}\Rightarrow x=k\pi +\frac{\pi }{4}(*)$ $\Rightarrow \operatorname{Cos}x\ne 0\Rightarrow x\ne k\pi +\frac{\pi }{2}\xrightarrow{(*)}x=k\pi +\frac{\pi }{4}$