![image](https://tex.z-dn.net/?f=%5Csin2x-2%5Csin%5E2x%3D4%5Csin+x-4%5Ccos+x%3B%5C%5C%0A2%5Csin+x%5Ccos+x-2%5Csin%5E2x%3D4%5Csin+x-4%5Ccos+x%3B%5C%5C%0A%5Csin+x%5Ccos+x-%5Csin%5E2x%3D2%5Csin+x-2%5Ccos+x%3B%5C%5C%0A%5Ccos+x%5Ccdot%28%5Csin+x%2B2%29%3D%5Csin+x%5Ccdot%28%5Csin+x%2B2%29%3B%5C%5C%0A%5Cforall+x%3A%5C+%5C+%5Csin+x%3E0%3B%5C%5C%0A%5Ccosx%3D%5Csin+x%3B%5C%5C%0Atgx%3D1%3B%5C%5C%0Ax%3D%5Cfrac%5Cpi4%2B%5Cpi+n%2C%5C+n%5Cin+Z)
0;\\
\cosx=\sin x;\\
tgx=1;\\
x=\frac\pi4+\pi n,\ n\in Z" alt="\sin2x-2\sin^2x=4\sin x-4\cos x;\\
2\sin x\cos x-2\sin^2x=4\sin x-4\cos x;\\
\sin x\cos x-\sin^2x=2\sin x-2\cos x;\\
\cos x\cdot(\sin x+2)=\sin x\cdot(\sin x+2);\\
\forall x:\ \ \sin x>0;\\
\cosx=\sin x;\\
tgx=1;\\
x=\frac\pi4+\pi n,\ n\in Z" align="absmiddle" class="latex-formula">