The formula of $ \cos(2t)\, $ = $ \frac{e^{2jt}+e^{-2jt}}{2}\, $.
We know the response of $ e^{2jt}\, $ is $ te^{-2jt}\, $ and the response of $ e^{-2jt}\, $ is $ te^{2jt}\, $.
So with an input of cos(2t),we will get the output as :
$ \frac{te^{2jt}+te^{-2jt}}{2}\, $
$ =t\frac{e^{2jt}+e^{-2jt}}{2}\, $
$ =t\cos(2t)\, $ ,which is the output.
