$2\operatorname{cosx}\left( \operatorname{cosx}-\operatorname{sinx} \right)=1\Rightarrow 2{{\cos }^{2}}x-2\operatorname{sinx}\operatorname{cosx}=1\Rightarrow 2{{\cos }^{2}}x-1=2\operatorname{sinx}\operatorname{cosx}$ $\Rightarrow \cos 2x=\sin 2x$ $\left( k\in z \right)\Rightarrow \tan 2x=1\Rightarrow 2x=k\pi +\frac{\pi }{4}\Rightarrow x=\frac{k\pi }{2}+\frac{\pi }{8}$