Sin5x-Sinx expressed as a product is

2cos3xsin2x

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2cos2xsin3x

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2sin3xcos2x

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2sin2xcos3x

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Solution

The correct option is A
2cos3xsin2x

We know that sinA-sinB = 2cos((A+B)/2)sin((A-B)/2)

Using this and substituting, A=5x and B= x we get

Sin5x-Sinx=2 cos3xsin2x

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