hoặc là thế này :
$pt\Leftrightarrow cos^7x+sin^5x+\frac{1}{2}cos^5xsin2x+\frac{1}{2}sin^3xsin2x=cosx+sinx$
$\Leftrightarrow cos^7x+cos^6xsinx+sin^5x+sin^4xcosx=cosx+sinx$
$\Leftrightarrow cos^6x(cosx+sinx)+sin^4x(sinx+cosx)=cosx+sinx$
$\Leftrightarrow (cosx+sinx)(cos^6x+sin^4x-1)=0$
$\Leftrightarrow (cosx+sinx)(cos^6x+(1-cos^2x)^2-1)=0$
$\Leftrightarrow (cosx+sinx)(cos^6x+cos^4x-2cos^2x)=0$
$\Leftrightarrow (cosx+sinx)cos^2x(cos^2x-1)(cos^2x+2)=0$