[latex]2sin( \frac{ \pi }{2}-x) cos( \frac{ \pi }{2}+x)= \sqrt{3} cosx[/latex]

[latex]2\sin( \frac{\pi}{2} -x)\cos(\frac{\pi}{2}+x)= \sqrt{3} \cos x \\ -2\cos x\sin x-\sqrt{3}\cos x=0 \\ -\cos x(2\sin x-\sqrt{3})=0 \\ \left[\begin{array}{ccc}\cos x=0\\ \sin x= \frac{\sqrt{3}}{2} \end{array}\right\to \left[\begin{array}{ccc}x_1= \frac{\pi}{2} +\pi n ,n \in Z \\ x_2=(-1)^k\cdot \frac{\pi}{3} + \pi k, k \in Z\end{array}\right[/latex]