Question

Prove that sin 3x = 3 sin x - 4 sin^3x.​

Answer 1

Answer:

required to prove

sin 3x= 3sin x-4 sin^3 x

proof:

sin3x =sin(2x+x)

=sin2x cos x+ sin x cos 2x

= 2sinx cosx ×cosx +sin x(1- 2sin^2x)

=2sin x ×cos^2× +sin x- 2sin^3 x

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

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

=3 sinx- 4sin^3x

hence proved