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