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Question

Sin3x+sin2xsinx=4sinxcosx2cos3x2

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Solution

sin3x+sin2xsinx=sin2x+sin3xsinx=sin2x+sin3xsinx[sinAsinB=2cos(A+B2)sin(AB2)]=2sinx cosx+sin3xsinx[sin2A=2sinA cos A]=2sinx cosx+2cos2x sinx=2sinx(cosx+cosx)=2sinx(2cos3x2cosx2)=4sinx cosx2cos3x2

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