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The number of...

Question

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

3

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4

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2

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1

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Solution

The correct option is A $1$
Given $sin 3 x = cos 2 x$
$⟹ cos (\frac{π}{2} - 3 x) = cos 2 x$
$⟹ \frac{π}{2} - 3 x = 2 n π \pm 2 x, n \in Z$
$⟹ \frac{π}{2} - 3 x = 2 n π + 2 x$ or $\frac{π}{2} - 3 x = 2 n π - 2 x$
$⟹ x = \frac{π}{10} - \frac{2 n π}{5}$ or $x = \frac{π}{2} - 2 n π$
In the interval $(\frac{π}{2}, π)$ , $x = \frac{9 π}{10}$
So number of solutions is $1$

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