The Basics of Linearity
In my opinion, the best way to solve this problem is to separate the cosine function as a sum of complex exponentials as follows.
$ cos(x)=\frac{1}{2}\left[e^{jx}+e^{-jx}\right] $
In the homework assignment, we are given the following two responses to the system.
$ e^{2jt}\rightarrow t e^{-2jt} $ and
$ e^{-2jt}\rightarrow t e^{2jt} $.
The response of the system turns out to be:
$ t cos(2t) $
