Question 710571
  formula for cox( x+y) cos(x-y) = cos ^2 (y) - sin^2( x)

 here cos (60-A) cos (60+A) = cos^2(A)-  sin^2 (60)
                            = cos ^2 (A)  - 3/4
        now cos A cos (60-A) cos (60+A  = cos A ( cos^2 (A) - 3/4)
\                                        = 1/4 (  4 cos ^3 (a) - 3 cos A)
{since  4 cos ^3 (a) - 3 cos A = cos 3A  }
                                         = 1/4 ( cos 3A)
hence proved