Provided that:
(1) $ e^{j2t}\ $ ----------> System ----------> $ te^{-2jt}\ $
(2) $ e^{-j2t}\ $----------> System ----------> $ te^{2jt}\ $
(3) The System is Linear.
The following should hold true:
(1)$ e^{j2t} + e^{-j2t}\ $ ----------> System -----------> $ te^{-2jt} + te^{2jt}\ $
(2)$ {e^{j2t} + e^{-j2t}\over 2} $ ----------> System -----------> $ {te^{-2jt} + te^{2jt}\over 2} $
The Key to approach this problem is: What is $ \cos 2t\ $?
(1) $ \cos 2t\ = {e^{j2t} + e^{-j2t} \over 2} $ by Euler's Formalas.
(2) The response to (1) is $ {te^{-2jt} + te^{2jt}\over 2} $
It is unnecessary to say this but it is $ t\ \cos 2t\ $
