[latex] \left \{ {{x+y= \pi } \atop {sin^{2}x+sin^{2}y=1 }} \right. [/latex]

[latex]x+y=\pi[/latex] [latex]y=\pi-x[/latex] [latex]sin^2 x+sin^2 y=1[/latex] [latex]sin^2 x+sin^2 (\pi-x)=1[/latex] [latex]sin^2 x+sin^2 x=1[/latex] [latex]2sin^2 x=1[/latex] [latex]sin^2 x=\frac{1}{2}[/latex] [latex]\frac{1-cos(2x)}{2}=\frac{1}{2}[/latex] [latex]cos(2x)=0[/latex] [latex]2x=\frac{\pi}{2}+\pi*k[/latex] [latex]x=\frac{\pi}{4}+\frac{\pi*k}{2}[/latex] k є Z [latex]y=\pi-x=\frac{3\pi}{4}+\frac{\pi*k}{2}[/latex]