Rewrite sin3 x as an equivalent expression that does not con

Rewrite sin^3 x as an equivalent expression that does not contain powers of trigonom functions greater than 1. 3/4 sinx + 1/4 sin 2x 3/4 sin x 3/4 sin x - 1/4 sin 3x 3/4 sin x + 1/2 sin 2x - 1/4 sin 3x

Solution

sin³x

to arrive at this, let us consider sin3x

sin3x = sin(2x + x) = sin(2x)cosx + cos(2x)sinx

and sin2x = 2sinx cos x

cos2x = 1 - 2sin²x

therefore, sin3x = (2sin x cos²x) + sinx - 2sin³x

=> 2sinx - 2sin³x + sinx - 2sin³x

[since cos²x = 1 - sin²x]

=> sin3x = 3sinx - 4sin³x

therefore, sin³x = (3/4)sinx - (1/4)sin3x [option C].