The number of solutions of $\cos 2 heta=\sin heta$ in $(0,2 \pi)$ are

Question

The number of solutions of $\cos 2 	heta=\sin 	heta$ in $(0,2 \pi)$ are

Aicharya · Accepted Answer

$\begin{aligned} & \cos 2 	heta=\sin 	heta \ & 	herefore 1-2 \sin ^2 	heta=\sin 	heta \Rightarrow 2 \sin ^2 	heta+\sin 	heta-1=0 \ & 	herefore(2 \sin 	heta-1)(\sin 	heta+1)=0 \Rightarrow \sin 	heta=\frac{1}{2},-1 \end{aligned}$ We have $	heta \in(0,2 \pi)$ $	herefore$ Possible values of $	heta$ are $\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{3 \pi}{6}$

The number of solutions of $\cos 2 \theta=\sin \theta$ in $(0,2 \pi)$ are

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