The Basics of Linearity
$ e^{(2jt)} $--->[linear system]--->$ te^{(-2jt)} $
and that
$ e^{(-2jt)} $--->[linear system]--->$ te^{(2jt)} $
we can rewrite $ cos(2t) $ as $ 0.5 * (e^{(2jt)}+e^{(-2jt)}) $
knowing that for any x1(t) and x2(t) yielding y1(t) and y2(t) respectively when passed through a linear system that A*x1(t) + B*x2(t) yields A*y1(t) + B*y2(t) we can change A and B to 0.5 thus
$ cos(2t) $--->linear system ---> $ 0.5t * (e^{(2jt)}+e^{(-2jt)}) $ or $ tcos(2t) $
