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Question
Express the following as the sum or difference of sines and cosines:
2 cos 7x cos 3x
Solution
\[2\left( \cos 7x \right) \left( \cos 3x \right)\]
\[ = \cos \left( 7x + 3x \right) + \cos \left( 7x - 3x \right) \left[ \because 2 \cos A \cos B = \cos(A + B) + \cos(A - B) \right]\]
\[ = \cos 10x + \cos 4x\]
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