Помогитееее[latex]sinx +cosx ^{2} \frac{x}{2} =sin^{2} \frac{x}{2} [/latex]

[latex]sin x+cos^2 \frac{x}{2}=sin^2 \frac{x}{2};[/latex] [latex]sin x+cos^2 \frac{x}{2}-sin^2 \frac{x}{2}=0[/latex] [latex]sin x+cos(2*\frac{x}{2})=0[/latex] [latex]sin x+cos x=0[/latex] [latex]\frac{1}{\sqrt{2}}sin x+\frac{1}{\sqrt{2}}cos x=0[/latex] [latex]sin xcos \frac{\pi}{4}+sin \frac{\pi}{4}cos x=0[/latex] [latex]sin(x+\frac{\pi}{4})=0[/latex] [latex]x+\frac{\pi}{4}=\pi*k[/latex] [latex]x=-\frac{\pi}{4}+\pi*k[/latex] k є Z