$ \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 t(\frac{e^{-2jt} + e^{2jt}}{2}) = t\cos{2t} $
