Решите уравнение sin 5x + sin x + 2[latex] sin^{2} [/latex] x = 1

[latex]sin 5x + sin x + 2 sin^{2} x = 1[/latex] [latex]sin5x+sinx=2sin3xcos2x[/latex] [latex]1-2sin^2x=cos2x[/latex] [latex]2sin3xcos2x-cos2x=0[/latex] [latex]cos2x(2sin3x-1)=0[/latex] [latex]cos2x=0[/latex] [latex]x= \frac{ \pi n}{4} [/latex] и[latex]sin3x= \frac{1}{2} [/latex] ⇒⇒[latex] x= \frac{ \pi }{18} + \frac{2}{3} \pi n[/latex][latex] x= \frac{5}{18} \pi+ \frac{2}{3} \pi Пn[/latex]