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The number of solutions of the pair of equations $2 \sin ^2 \theta-\cos 2 \theta=0$ and $2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
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The correct answer is:
two
two
$2 \sin ^2 \theta-\cos 2 \theta=0 \Rightarrow \sin ^2 \theta=\frac{1}{4}$
Also, $2 \cos ^2 \theta=3 \sin \theta \Rightarrow \sin \theta=\frac{1}{2}$
$\Rightarrow$ Two solutions in $[0,2 \pi]$.
Also, $2 \cos ^2 \theta=3 \sin \theta \Rightarrow \sin \theta=\frac{1}{2}$
$\Rightarrow$ Two solutions in $[0,2 \pi]$.
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