Answer:
Option B
Explanation:
Consider the equations
$\cos 2 \theta=\sin \theta$
$\Rightarrow$ $1-2\sin^{2} \theta=\sin \theta$
$\Rightarrow$ $2 \sin^{2} \theta+\sin \theta-1=0$
$\Rightarrow$ $2 \sin \theta( \sin \theta+1)-1(\sin \theta+1)=0$
$\Rightarrow$ $(\sin \theta+1)(2 \sin \theta-1)=0$
$\Rightarrow$ $\sin \theta=-1 $ or $\sin \theta=\frac{1}{2}$
$\Rightarrow$ $\theta=\frac{3 \pi}{2}$ or $\theta= \frac{\pi}{6},\frac{5 \pi}{6}$
$[\because \theta \in (0,2\pi)]$
Thus, number of solutions of the given equation is 3
