We study a combined effect of wave trapping due to oppositely propagating narrow band whistler mode waves and discuss its dependence on the background plasma density. In the case where forward and backward traveling whistler mode waves coexist, rapid scattering of resonant electrons occurs owing to the overlapping of diffusion curves of both waves. Simulation results show that the low-density plasma condition, where the electron plasma frequency is close to the electron gyrofrequency, is favorable for the significant resonant scattering of high energetic electrons. The results of the present study suggest that the combined effect plays an important role in energizing relativistic electrons in the equatorial region of the Earth's inner magnetosphere during the recovery phase of geomagnetic storms.