If the r.v.s X1 and X2 are independent, then show that eit(X1+X2) = eitX1 ( eitX2, t

If the r.v.s X1 and X2 are independent, then show that
εeit(X1+X2) = εeitX1 ( εeitX2, t ( (,
and by induction,
εeit(X1+...+xk) = εeitX1 ( ... ( εeitXk, t ( (
for the independent r.v.s x1, ...., Xk.
Write eit(X1+X2) = eitX1 ( eitx2 = [cos(tX1)+i sin (tX1)] ( [cos(tX2) + i sin (tX2)] and use Proposition 1.