From the formula for sin (2t + t) find sin 3t in terms of sin t.

Answer 1

Sin3x    = sin (2x+x)

              = sin2x cosx + sinx cos2x

              = 2 sinx cosx cosx + sinx ( 1-2sin²x)

              = 2 sinx cos²x + sinx – 2sin³x

              = 2 sinx (1 – sin²x) + sinx – 2 sin³x

              = 2 sinx –2 sin²x sinx + sinx –2 sin³x

              = 3 sinx – 4 sin³x