A linear system is a mathematical model of a system based on the use of a linear operator. A system is called "linear" if for any constants a,b complex number and for any inputs x1(t) and x2(t) yielding output y1(t),y2(t) respectively the response to a.x1(t)+b.x2(t) is a.y1(t)+b.y2(t)
Now we are given the information that,
$ {e^{2jt}} $$ {\longrightarrow} $$ {te^{-2jt}} $
i.e
$ {cos(2t)+jsin(2t)} $$ {\longrightarrow} $$ {t*(cos(2t)-jsin(2t))} $
also,
$ {e^{-2jt}} $$ {\longrightarrow} $$ {te^{2jt}} $
i.e
$ {cos(2t)-jsin(2t)} $$ {\longrightarrow} $$ {t*(cos(2t)+jsin(2t))} $
Now, let us take the arbitiary constants such that a=b=1/2.
Therefore, $ {{1/2*({cos(2t)+jsin(2t)})}+{1/2*({cos(2t)-jsin(2t)})}={1/2(t*({cos(2t)-jsin(2t)}))}+{1/2(t*({cos(2t)+jsin(2t)}))}} $
This gives cos(2t)$ {\longrightarrow} $ tcos(2t)
