Linearity
If a linear system has a response to $ exp(2jt) $ of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t).
Explanation:
The system seems to have the following characteristics:
x(t) --> SYSTEM --> t*y(-t)
Therefore, if we put the change the input from x(t) (above) to cos(2t), then it should output the signal t*cos(-2t).
