According to the following equations :
$ exp(2jt)=t* exp(-2jt) $
and
$ exp(-2jt)=t * exp(2jt) $
we see that the system equation is:
$ x(-t)->t*x(t) $
in case of cosine function
$ cos(t)->t*cos(t) $
$ cos(-t)->*cos(-t) $ thus $ cos(-t)=t*cos(t) $hence it is an even function
