Total number of solutions of $sin x . tan 4 x = cos x$ belonging to $(0, π)$ are:

4

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5

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7

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8

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Solution

The correct option is C $5$
$sin x tan 4 x = cos x$
$\Rightarrow sin x sin 4 x = cos x cos 4 x$
$\Rightarrow \frac{1}{2} (cos 3 x - cos 5 x) = \frac{1}{2} (cos 5 x + cos 3 x)$
$\Rightarrow cos (5 x) = 0 \Rightarrow 5 x = (2 n + 1) \frac{π}{2}$
$\Rightarrow x = (2 n + 1) \frac{π}{10}$
Hence there are $5$ values in $(0, π)$

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