Question

2cos(x-11П/2)cosx=sinx

Answer 1

$2\cos (x- \frac{11 \pi }{2} )\cos x=\sin x \\ -2\sin x\cos x=\sin x \\ -2\sin x\cos x-\sin x=0 \\ -\sin x(2\cos x+1)=0 \\ \left[\begin{array}{ccc}\sin x=0\\ \cos x=- \frac{1}{2} \end{array}\right\to \left[\begin{array}{ccc}x_1=\pi k, k \in Z\\ x_2=\pm \frac{2 \pi }{3}+2 \pi n,n \in Z \end{array}\right$