Prove the identity cos(3x)=cos^3(x)-3sin^2(x)cos(x), step by step.

Cos(A+B) = cosAcosB - sinAsinB
cos(3x) = cos(x+2x)
cos(x+2x)= cosxcos2x-sinxsin2x
cos2x = 2cos^2 (x) - 1
sin(2x) = 2sin(x)cos(x)
by putting the values we get
cos(x+2x)= cosx*cos2x-sinx*sin2x=cosx*(2cos^2 (x) - 1) -(sinx*2sin(x)cos(x))
                                                          =cos^3(x)-3sin^2(x)cos(x)
hope it helps

Answer is a not really sure tho