How do I derive cos2a

It said to use the fact that sin2a=sin(A+A) and I did. I got cos(A+A) then I used the composite argument and it became cos^2A-Sin^2A. Is this the final answer or is there a way to derive it further? If there is a way to derive this further, could someone explain it to me? Thanks! :D

yes , you're correct
= cos^2A-Sin^2A or 2cos^2A - 1 or 1 - 2Sin^2A