Решите уравнение: 2sin^2 (x) - cos (2x) = 1.

[latex]2sin^2 x - cos 2x = 1[/latex] [latex]2sin^2 x = 1+cos2x[/latex] [latex]2sin^2 x = 2cos^2x[/latex] [latex]sin^2 x = cos^2x[/latex] [latex]sin^2 x -cos^2x=0[/latex] [latex] -(cos^2x-sin^2x)=0[/latex] [latex]cos2x=0[/latex] [latex]2x= \frac{ \pi }{2} + \pi n,[/latex] [latex]n[/latex] ∈ [latex]Z[/latex] [latex]x= \frac{ \pi }{4} + \frac{\pi n}{2} ,[/latex] [latex]n[/latex] ∈ [latex]Z[/latex]