1-cos(п+x)-sin(3п/2 + x/2)=0

Решите задачу:

$1-cos(\pi +x)-sin(\frac{3\pi}{2}+\frac{x}{2})=0\\ 1+cosx-cos\frac{x}{2} =0\\ cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}-cos\frac{x}{2}+1=0\\ cos^{2}\frac{x}{2}-(1-cos^{2}\frac{x}{2})-cos\frac{x}{2}+1=0\\ cos^{2}\frac{x}{2}-1+cos^{2}\frac{x}{2}-cos\frac{x}{2}+1=0\\ 2cos^{2}\frac{x}{2}-cos\frac{x}{2}=0\\ cos\frac{x}{2}(2cos\frac{x}{2}-1)=0\\ 1)cos\frac{x}{2}=0\\ \frac{x}{2}=\frac{\pi}{2}+\pi n\\ x=\pi + 2\pi n \\ 2) 2cos\frac{x}{2}-1=0\\ cos\frac{x}{2}=\frac{1}{2}\\ \frac{x}{2}=+\ -\frac{\pi}{3}+2\pi n\\ x=+\ - \frac{2\pi}{3}+4\pi n$