pt<=> 1+\sin \frac{x}{2}\sin x-2\cos2 \frac{x}{2}\sin \frac{x}{2}-(\sin \frac{x}{2}+\cos \frac{x}{2})^2<=>1+\sin \frac{x}{2}\sin x-2\cos2 \frac{x}{2}\sin \frac{x}{2}-\sin2 \frac{x}{2}-\cos2 \frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2}=0<=>(1-(\sin2 \frac{x}{2}+\cos2 \frac{x}{2})+2\sin2 \frac{x}{2}\cos \frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2}(\cos \frac{x}{2}+1)=0<=>2\sin \frac{x}{2}\cos \frac{x}{2}(\sin \frac{x}{2}-\cos \frac{x}{2}-1)=0+2\sin \frac{x}{2}\cos \frac{x}{2}=0-\sin \frac{x}{2}=0\rightarrow x=2k\Pi -\cos \frac{x}{2}=0\rightarrow x=\frac{\Pi }{4}+\frac{k\Pi }{2}+\sin \frac{x}{2}-\cos \frac{x}{2}-1=0\Leftrightarrow \sqrt{2}\sin x\frac{x}{2}-\frac{\Pi }{4}=1\Leftrightarrow x=\frac{3\Pi }{4}+2k\Pi
pt
$<=> 1+\sin \frac{x}{2}\sin x-2\cos2 \frac{x}{2}\sin \frac{x}{2}-(\sin \frac{x}{2}+\cos \frac{x}{2})^2
$$<=>1+\sin \frac{x}{2}\sin x-2\cos2 \frac{x}{2}\sin \frac{x}{2}-\sin2 \frac{x}{2}-\cos2 \frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2}=0
$$<=>(1-(\sin2 \frac{x}{2}+\cos2 \frac{x}{2})+2\sin2 \frac{x}{2}\cos \frac{x}{2}-2\sin \frac{x}{2}\cos \frac{x}{2}(\cos \frac{x}{2}+1)=0
$$<=>2\sin \frac{x}{2}\cos \frac{x}{2}(\sin \frac{x}{2}-\cos \frac{x}{2}-1)=0
$$+2\sin \frac{x}{2}\cos \frac{x}{2}=0
$$-\sin \frac{x}{2}=0\rightarrow x=2k\Pi-\cos \frac{x}{2}=0\rightarrow x=\frac{\Pi }{4}+\frac{k\Pi }{2}
$$+\sin \frac{x}{2}-\cos \frac{x}{2}-1=0\Leftrightarrow \sqrt{2}\sin x\frac{x}{2}-\frac{\Pi }{4}=1\Leftrightarrow x=\frac{3\Pi }{4}+2k\
pi
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