Through the system, the following transformations are made:
$ e^{2jt} \to t e^{-2jt} $
$ e^{2jt} \to t e^{-2jt} $
By observation, we know the system multiplies by t and is time reversing.
Given that:
$ \cos{t} = \frac{e^{jt} + e^{-jt}}{2} $
Then
$ \cos{2t} \to t \frac{e^{-2jt} + e^{2jt}}{2} = t \cos{t} $
