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 (\frac{x}{2}-\frac{\Pi }{4})2=1\Leftrightarrow x=\frac{3\Pi }{4}+2k\pi$