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Question
Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa
Solution
\[2\left( \cos 3x \right) \left( \sin 2x \right)\]
\[ = \sin \left( 3x + 2x \right) - \sin \left( 3x - 2x \right) \left[ \because 2 \cos A \sin B = \sin(A + B) - \sin(A - B) \right]\]
\[ = \sin 5x - \sin x\]
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