FullSimplify[Re[E^(I k Rr)(-I + k Rr) * Cos[Ttheta] ], Element[{k,Rr, Ttheta}, Reals],TimeConstraint->10] // Timing
Simplify[Re[E^(I k Rr)(-I + k Rr) Cos[1]], Element[{k,Rr, Ttheta}, Reals]]
Expand[Re[E^(I k Rr)(-I + k Rr) Cos[1]], Element[{k,Rr, Ttheta}, Reals]]
FullSimplify[Re[E^(I k Rr)(-I + k Rr) Cos[1]], Element[{k,Rr, Ttheta}, Reals]]
Simplify[Re[Cos[Ttheta]], Element[Ttheta, Reals]]