JEE Main 2025 — Trigonometric Equations Question with Solution

$\begin{aligned} & 2 \sin ^2 \theta=\cos 2 \theta \\ & 2 \sin ^2 \theta=1-2 \sin ^2 \theta \\ & 4 \sin ^2 \theta=1 \\ & \sin ^2 \theta=\frac{1}{4} \\ & \sin \theta= \pm \frac{1}{2} \\ & 2 \cos ^2 \theta=3 \sin \theta \\ & 2-2 \sin ^2 \theta+3 \sin \theta-2=0 \\ & (2 \sin \theta-1)(2 \sin \theta-2)=0 \\ & \sin \theta=\frac{1}{2} \end{aligned}$ so common equation which satisfy both equations is $\sin \theta =\frac{1}{2}$ $\theta =\frac{\pi }{6},\frac{5\pi }{6}(\theta \in [0,2\pi ])$ Sum $=\pi$