Question:
sin 3x + sin 2x - sin x = 4sin x cos(x/2) cos(3x/2)
Answer:
Given sin 3x + sin 2x - sin x
=> sin 3x - sin x + sin2x
=> 2*cos(3x+x)/2 * sin(3x-x)/2 + sin2x
=> 2*cos2x*sinx + 2*sinx*cosx (sin2x = 2*sinx*cosx)
=> 2*sinx*(cos2x + cosx)
=> 2*sinx*2*cos(2x+x)/2 *cos(2x-x)/2
=> 4*sinx*cos(3x/2) * cos(x/2)
So sin 3x + sin 2x - sin x = 4*sinx*cos(x/2) *cos(3x/2)
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