\(pt\Leftrightarrow\left(cosx+sinx\right)\left(sin^2x+cos^2x-sinx.cosx\right)=cosx+sinx+sin2x\)
\(\Leftrightarrow\left(cosx+sinx\right)\left(1-sinx.cosx-1\right)=sin2x\)
\(\Leftrightarrow-\dfrac{1}{2}sin2x\left(cosx+sinx\right)=sin2x\)
\(\Leftrightarrow sin2x\left(cosx+sinx+2\right)=0\)
\(\Leftrightarrow sin2x\left[\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)+2\right]=0\)
\(\Leftrightarrow sin2x=0\)
\(\Leftrightarrow x=\dfrac{k\pi}{2}\)
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