The two functions given to us happen to be part of the breakdown of cos(2t).
$ cos(2t)=\frac{1}{2}e^{2jt}+\frac{1}{2}e^{-2jt} $
If the response to $ e^{2jt}=te^{-2jt} $ and $ e^{-2jt}=te^{2jt} $ then, cos(2t) -> System -> $ t\frac{1}{2}e^{-2jt} + t\frac{1}{2}e^{2jt} = tcos(2t) $
Referenced: Max Paganini
