Question

корень из 3*(sin x/2-cos x/2)*(cos x/2+sin x/2)=sin 2x
При [-п; п/2]

Answer 1

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