Sin^2(x)+cos(x) sin(x)-cos2x=0

[latex]sin^2(x)+cos(x) sin(x)-cos2x=0\sin^2(x)+cos(x) sin(x)-cos^2x+sin^2x=0\2sin^2x+sinxcosx-cos^2x=0\2tg^2x+tgx-1=0\tgx_{1,2}=frac{1^+_-3}{4}\tgx_1=1 tgx_2=-frac{1}{2}\x_1=frac{pi}{4}+pi n x_2=-arctgfrac{1}{2}+pi n;nin Z[/latex]