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Show thatsin3x+sin2xsinx=4sinxcosx2cos3x2

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Solution

sin3x+sin2xsinx=2cos2xsinx+sin2x
=2cos2xsinx+2sinxcosx
=2sinx(cosx+cos2x)
=2sinx(2cosx2cos3x2)
sin3x+sin2xsinx=4sinxcosx2cos3x2.

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