می‌دانیم $\cos 2x=2{{\cos }^{2}}x-1$، پس $2{{\cos }^{2}}x=1+\cos 2x$. $\cos 2x+2{{\cos }^{2}}x=0\Rightarrow \cos 2x+(1+\cos 2x)=0$ $\Rightarrow 2\cos 2x+1=0\Rightarrow \cos 2x=\frac{-1}{2}$ $\Rightarrow \cos 2x=\cos \frac{2\pi }{3}$ $\Rightarrow 2x=2k\pi \pm \frac{2\pi }{3}\Rightarrow x=k\pi \pm \frac{\pi }{3}$