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# The number of solutions of the pair of equations $2\sin^2\theta-\cos 2\theta=0$ and $\cos^2\theta-3\sin\theta=0$ in the interval $[0,2\pi]$ is

$(a)\;0\qquad(b)\;1\qquad(c)\;2\qquad(d)\;4$

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## 1 Answer

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$2\sin^2\theta-\cos 2\theta=0$
$2\sin^2\theta-(1-2\sin^2\theta)=0$
$4\sin^2\theta=1$

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