1+3sin^2x=2sin2x помогите

[latex]1+3sin^{2} x=2sin2x [/latex] [latex]sin^{2}x+cos^{2} x+3sin^{2} x=4sinx*cosx [/latex] [latex]4sin^{2} x-2sinx*cosx+cos^{2} x=0 |:cos^{2} x[/latex] [latex]4tg^{2} x-4tgx+1=0[/latex] Пусть tgx=а [latex]a^{2} -4a+1=0[/latex] [latex]D=(-4)^{2} -4*4=0[/latex] [latex]a= \frac{4}{8} = \frac{1}{2} [/latex] [latex]tgx= \frac{1}{2} [/latex] [latex]x=arctg \frac{1}{2} + \pi n[/latex] , n из множества Z