$2\operatorname{Cos}x(\operatorname{Cos}x-\operatorname{Sin}x)=1\Rightarrow 2{{\operatorname{Cos}}^{2}}x-2\operatorname{Sin}x\operatorname{Cos}x=1\Rightarrow 2{{\operatorname{Cos}}^{2}}x-1=2\operatorname{Sin}x\operatorname{Cos}x\Rightarrow \operatorname{Cos}2x=\operatorname{Sin}2x\xrightarrow{\div \operatorname{Cos}2x}\tan 2x=1=\tan \frac{\pi }{4}\Rightarrow 2x=k\pi +\frac{\pi }{4}\Rightarrow x=\frac{k\pi }{2}+\frac{\pi }{8}$