جواب کلی معادلهی $\cos \left( \pi -x \right)\sin \left( \frac{۳\pi }{۲}-x \right)-\sin \left( \pi +x \right)\cos \left( \frac{\pi}{۲}+x \right)=-{{\sin }^{۲}}\frac{۵\pi }{۴}$ کدام است؟$\left( k\in z \right)$
$\cos \left( \pi -x \right)=-\operatorname{cosx}$ $\sin \left( \frac{3\pi }{2}-x \right)=-\operatorname{cosx}$ $\sin \left( \pi +x \right)=-\operatorname{sinx}$ $\cos \left( \frac{\pi }{2}+x \right)=-\operatorname{sinx}$ $-{{\sin }^{2}}\frac{5\pi }{4}=-\frac{1}{2}\Rightarrow {{\cos }^{2}}x-{{\sin }^{2}}x=-\frac{1}{2}\Rightarrow \cos 2x=-\frac{1}{2}$ $\Rightarrow 2x=2k\pi \pm \frac{2\pi }{3}\Rightarrow x=k\pi \pm \frac{\pi }{3}$