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