2cos^2 x=1+2sin^2 x решите

[latex]2\cos^2x=1+2\sin^2x\\ 2\cos^2x-2\sin^2x=1\\ 2(\cos^2x-\sin^2x)=1\\ \\ \cos2x=0.5\\ 2x=\pm \frac{\pi }{3} +2\pi n,n \in \mathbb{Z}\\ \\ x=\pm \frac{\pi }{6} +\pi n,n \in \mathbb{Z}[/latex]