The frequency dependent scattering rate of generalized Drude model contains important information on the electronic structure and on scattering mechanism. In the present investigation, we study the frequency dependent scattering rate of cuprates (Mitrović-Fiorucci/Sharapov-Carbotte scattering rate) in the pseudogap phase using the non-constant energy dependent Yang-Rice-Zhang (YRZ) density of states. First, with the energy dependent density of states, the scattering rate shows a depression at low energy coming from the opening of the pseudogap. Second, the evolution of 1/τ(ω,T) with temperature shows the observed increase in scattering rate with temperature at lower frequencies and the temperature independence of 1 /τ(ω) at higher frequencies. Third, the signature of the thresholds due to the boson density of states and to the electronic density of states are also observed. These signatures are qualitatively in accord with the experiments.