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