Linearity
The System takes the input and gives the output as follows:
$ e^{2jt} \to System \to te^{-2jt}\! $
$ e^{-2jt} \to System \to te^{2jt}\! $
now,we know that $ cos(2t)=\frac{1}{2}e^{2jt} + \frac{1}{2}e^{-2jt} $
thus now from the above equations we can see that $ e^{2jt} $ converts to $ te^{-2jt} $ and $ e^{-2jt} $ converts to $ te^{2jt} $
thus $ cos(2t)=\frac{1}{2}e^{2jt} + \frac{1}{2}e^{-2jt} \to system \to \frac{1}{2}te^{-2jt}+ \frac{1}{2}te^{2jt}=t[\frac{1}{2}e^{-2jt}+ \frac{1}{2}e^{2jt}]=tcos(2t) $
