FullSimplify[Re[                                                (-I + k Rr)] Cos[Ttheta], Element[{k,Rr, Ttheta, t, omega}, Reals]]
FullSimplify[Re[E^(I (omega t - k Rr))                         ] Cos[Ttheta], Element[{k,Rr, Ttheta, t, omega}, Reals]]
ComplexExpand[Simplify[Re[E^(I (omega t - k Rr))(-I + k Rr)] Cos[Ttheta], Element[{k,Rr, Ttheta, t, omega}, Reals]]]