1)$PT\Leftrightarrow 2sin 2x.cos 2x- 2cos^{2} 2x+1=1+4(sin x-cos x)$$\Leftrightarrow 2cos 2x(sin 2x- cos 2x)=4(sin x-cos x)$
$\Leftrightarrow (cos x-sin x)(cos x+sin x)(sin 2x-cos 2x)=-2(cos x-sin x)$
$\Leftrightarrow (cos x- sin x)[(cos x+sin x)(sin 2x-cos 2x)+2]=0$