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Convert the following products into the sum or difference of sines and cosines: $$\text{2 sin}\; 5x\;\text {cos}\; x$$
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## QuestionMathsClass 11

Convert the following products into the sum or difference of sines and cosines: $$\text{2 sin}\; 5x\;\text {cos}\; x$$

As we know $$2 \sin A \cos B=\sin (A+B)+\sin (A-B),$$ we get
$$\therefore 2 \sin 5 x \cos x$$
$$= \sin (5 x+x)+\sin (5 x-x)$$
$$=\sin 6 x+\sin 4 x$$