Решите уравнение: sin(x+п/3)cos(x-п/6)=1

[latex]sin(x+\frac{\pi}{3})\cdot cos(x-\frac{\pi}{6})=1\\\\\frac{1}{2}(sin\frac{\pi}{2}+sin(2x+\frac{\pi}{6}))=1\\\\\frac{1}{2}(1+sin(2x+\frac{\pi}{6}))=1\\\\sin(2x+\frac{\pi}{6})=1\\\\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]