Решите уравнение 1+sin2x=cosx+sinx

1+sin2x=cosx+sinx\\ 1+2sinxcosx=cosx+sinx\\ 1+4sinxcosx+4sin^2xcos^2x=cos^2x+sin^2x+2sinxcosx\\ 1+4sinxcosx+(2sinxcosx)^2=1+sin2x\\ 0=(sin2x)^2+sin2x\\ sin2x(sin2x+1)=0\\ sin2x=0\iff 2x=k\pi\iff x=k\frac{{\pi}{2}\\ sin2x=-1\iff 2x=\frac{{3}{2})\pi+2k\pi\iff x=\frac{{3}{4}}\pi +k\pi