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Question
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Solution
\[\cos 12x + \cos 8x\]
\[ = 2\cos \left( \frac{12x + 8x}{2} \right) cos \left( \frac{12x - 8x}{2} \right) \left\{ \because \cos A + \cos B = 2\cos\left( \frac{A + B}{2} \right)\cos\left( \frac{A - B}{2} \right) \right\}\]
\[ = 2 \cos 10x \cos 2x\]
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