Mathematics - Trigonometric Equation Question with Solution | TestHub

$\begin{array}{rl}& 2{\sin }^2\theta =\cos 2\theta \\ & 2{\sin }^2\theta =1-2{\sin }^2\theta \\ & 4{\sin }^2\theta =1\\ & {\sin }^2\theta =\frac{1}{4}\\ & \sin \theta =\pm \frac{1}{2}\\ & 2{\cos }^2\theta =3\sin \theta \\ & 2-2{\sin }^2\theta +3\sin \theta -2=0\\ & (2\sin \theta -1)(2\sin \theta -2)=0\\ & \sin \theta =\frac{1}{2}\end{array}$ 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 $=\pi$