Question:
Prove that sin3x + sin2x - sinx = 4sinx *cos3x/2 * cosx/2
Answer:
Given sin3x + sin2x - sinx
= (sin 3x - sinx) + sin2x
= 2*sin (3x-x)/2 * cos(2x+x)/2 + sin2x
= 2*sinx * cos2x + sin2x
= 2*sinx * cos2x + 2*sinx*cosx
= 2sinx(cos2x + cosx)
= 2sinx{2*cos(2x+x)/2 * cos(2x-x)/2}
= 2sinx{2*cos 3x/2 * cos x/2}
= 4sinx * cos3x/2 * cos x/2
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