Prove The Identity

Question

cos(3x) = 4 cos³(x) - 3 cos(x)

To verify the​ identity, start with the left side and transform it to look like the right side. Choose the correct transformations and transform the expression at each step.

Answer 1

cos(3x)=cos(2x+x)=cos 2x cos x - sin 2x sinx= cos x(cos²x - sin²x) -2sin²x cos x

=cos³x -cos x sin²x - 2 sin²xcos x=cos³x -3sin²x cos x

=cos³x - 3(1-cos²x)cos x = 4 cos³x-3 cos x Q.E.D.