Решите уровнение)cos4x+2cos^2x=0

[latex]cos\ 4x+2cos^2x=0\\ (2cos^22x-1)+(1+cos\ 2x)=0\\ 2cos^22x+cos\ 2x=0\\ cos\ 2x(2cos\ 2x+1)=0\\ \left[ \begin{matrix} cos\ 2x=0\\ 2cos\ 2x+1=0 \end{matrix}\right\ <=> \left[ \begin{matrix} cos\ 2x=0\\ cos\ 2x=-\frac{1}{2} \end{matrix}\right\ <=> \\ \left[ \begin{matrix} 2x=\frac{\pi}{2}+\pi k\\ 2x=\pm \frac{2\pi}{3}+2\pi m \end{matrix}\right\ <=> \left[ \begin{matrix} x=\frac{\pi}{4}+\frac{\pi k}{2}\\ x=\pm \frac{\pi}{3}+\pi m \end{matrix}\right.[/latex] [latex]Ombem:\ \frac{\pi}{4}+\frac{\pi k}{2};\ \pm \frac{\pi}{3}+\pi m;\ k \in Z,\ m \in Z.[/latex]