sorry, typo in the first line {as you said, it should be cos4A not cos2A}, but after that it should be alright.
I used the identity that
cos(2x)=1-2sin^2(x)
hence:
cos(4x)=1-2sin^2(2x)
please correct me if I have done something wrong in the rest
btw, does anyone know how to get rid of the br...