Sin^4 x + cos^4 x=sin 2x

[latex]sin^4 x+cos^4 x=sin (2x)[/latex] [latex](sin^2 x+cos^2 x)^2-2sin xcos x-sin(2x)=0[/latex] [latex]1^2-sin(2x)-sin(2x)=0[/latex] [latex]1-2sin(2x)=0[/latex] [latex]sin(2x)=\frac{1}{2}[/latex] [latex]2x=(-1)^k*\frac{\pi}{6}+\pi*k[/latex] k є Z [latex]x=(-1)^k*\frac{\pi}{12}+\frac{\pi*k}{2}[/latex] k є Z