$ \cos{2t} = \frac{e^{2jt} - e^{-2jt}}{2} $
Since we know,
$ e^{2jt} \Longrightarrow System \Longrightarrow te^{-2jt} $
and
$ e^{-2jt} \Longrightarrow System \Longrightarrow te^{2jt} $
then
$ \cos{2t} \Longrightarrow System \Longrightarrow \frac{te^{-2jt} - te^{2jt}}{2} = t\cos{2t} $
