The number of solutions of $\sin 3 x = \cos 2 x$ in the interval $(\frac{π}{2}, π)$ is

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answer is B.

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Detailed Solution

$\sin 3 x = \cos 2 x \Rightarrow 3 sinx - 4 \sin^{3} x = 1 - 2 \sin^{2} x$
$4 \sin^{3} x - 2 \sin^{2} x - 3 sinx + 1 = 0$
$\sin x = 1, \frac{- 2 \pm 2 \sqrt{5}}{8} In (\frac{π}{2}, π) \sin x = \frac{- 2 + 2 \sqrt{5}}{8}$

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