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Convert each of the following products into the sum or difference of sines and cosines:$$2 \sin \;3x \;\sin x$$
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## QuestionMathsClass 11

Convert each of the following products into the sum or difference of sines and cosines:$$2 \sin \;3x \;\sin x$$

Using $$2 \sin A \sin B=\cos (A-B)-\cos (A+B),$$ we obtain
$$2 \sin 3 x \sin x=\cos (3 x-x)-\cos (3 x+x)=\cos 2 x-\cos 4 x$$