Решите уравнение 1/2cos2x+([latex] \sqrt{3} [/latex])/2sin2x=1

[latex] \frac{1}{2}cos2x+\frac{\sqrt3}{2} sin2x=1\\\\sin\frac{\pi}{6}\cdot cos2x+cos\frac{\pi}{6}\cdot sin2x=1\\\\sin(2x+\frac{\pi}{6})=1\\\\2x+\frac{\pi}{6}=\frac{\pi}{2}+2\pi n,\; n\in Z\\\\2x=-\frac{\pi}{6}+\frac{\pi}{2}+2\pi n,\; n\in Z\\\\2x=\frac{\pi}{3}+2\pi n,\; n\in Z\\\\x=\frac{\pi}{6}+\pi n ,\; n\in Z[/latex]