Statement 1: The number of common solutions of the trigonometric equations 2 sin^2 θ- cos 2 θ=0 and 2 cos^2 θ-3 sin θ=0 in the interval [0,2 π] is…

Statement $\displaystyle 1$ : The number of common solutions of the trigonometric equations $\displaystyle 2 \sin ^2 \theta-\cos 2 \theta=0$ and $\displaystyle 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $\displaystyle [0,2 \pi]$ is two : Statement $\displaystyle 2$: The number of solutions of the equation, $\displaystyle 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $\displaystyle [0, \pi]$ is two.