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  4. Total number of solutions of equation sin x . tan 4 x= cos x belonging to (-π, 2 π) are:

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Q. Total number of solutions of equation $\sin x . \tan 4 x=\cos x$ belonging to $(-\pi, 2 \pi)$ are:

Trigonometric Functions

Solution:

$\sin x \cdot \tan 4 x=\cos x $
$\Rightarrow \sin x \sin 4 x=\cos x \cos 4 x$
$\Rightarrow \cos 5 x=0 $
$\Rightarrow$ five solutions.

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