Prove that: sin3x + sin2x - sinx = 4sinxcos(x/2)cos(3x/2)

LHS = sin3x + sin2x - sinx
= 2sin((3x+2x)/2)cos((3x-2x)/2) - sinx
= 2sin(5x/2)cos(x/2) - sinx
= 2sin(5x/2)cos(x/2) - 2sin(x/2)cos(x/2)
= 2cos(x/2)[sin(5x/2) - sin(x/2)]
= 2cos(x/2)[2cos((5x/2 + x/2)/2)sin((5x/2 - x/2)/2)]
= 2cos(x/2)[2cos(3x/2)sin(x)]
= 4cos(x/2)cos(3x/2)sinx
= 4sinxcos(x/2)cos(3x/2)
= RHS