Prove the identity 8 sin 3x sin x 34sin2x Solutionsin3x si

Prove the identity: 8. sin 3x = sin x (3-4sin2x)

sin3x = sinx( 3 - 4sin^2x)

sin3x = sin(2x+x)

= sin2xcosx + cos2xsinx

= 2sinxcos^2x + (1-2sin^2x)sinx

= 2sinxcos^2x + sinx - 2sin^3x

= 2sinx(1-sin^2x) + sinx -2sin^3x

= 2sinx - 2sin^3x + sinx - 2sin^3x

= -4sin^3x +3sinx

= sinx(3 - 4sin^2x)

= RHS