The number of solutions of sin 3x = cos 2x, in the interval (π/2,π) is

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The number of solutions of sin 3x = cos 2x, in the interval (π/2,π) is

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answer is D.

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Detailed Solution

$\sin 3 x = \cos 2 x \Rightarrow \sin 3 x = \sin (\frac{π}{2} - 2 x) \Rightarrow 3 x = nπ + (- 1)^{n} (\frac{π}{2} - 2 x)$
$\Rightarrow 3 x = 2 nπ + (\frac{π}{2} - 2 x) or 3 x = (2 n + 1) π - (\frac{π}{2} - 2 x) \Rightarrow 5 x = (4 n + 1) \frac{π}{2} or x = (4 n + 1) \frac{π}{2}$
$\Rightarrow x = (4 n + 1) \frac{π}{10} or x = (4 n + 1) \frac{π}{2} where n \in Z, x \in (\frac{π}{2}, π) \Rightarrow x = \frac{2 π}{10}$
$∴$ The number of solutions : 1.