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Question
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Solution
\[\sin 12x + sin 4x\]
\[ = 2\sin \left( \frac{12x + 4x}{2} \right) \cos\left( \frac{12x - 4x}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2 \sin 8x \cos 4x\]
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