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{2t} $

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