Probably could have put a few more steps in there for a full written solution, but it looks good to me. --Kathleen Schremser
Could have directly written that
$ cos(2t)=\frac{1}{2}e^{2jt} + \frac{1}{2}e^{-2jt} $
as it is a standard result would have saved you some unnecessary steps but the solution is nice
--sourabh ranka