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# Express Each of the Following as the Product of Sines and Cosines: Sin 5x − Sin X - Mathematics

#### Question

Express each of the following as the product of sines and cosines:
sin 5x − sin x

#### Solution

$\sin 5x - \sin x$
$= 2\sin \left( \frac{5x - x}{2} \right) \cos \left( \frac{5x + x}{2} \right) \left\{ \because \sin A - \sin B = 2\sin\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \right\}$
$= 2 \sin 2x \cos 3x$

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