While the cosmic soft X-ray background is very likely to originate from individual Seyfert galaxies, the origin of the cosmic hard X-ray and MeV gamma-ray background is not fully understood. It is expected that Seyferts including Compton thick population may explain the cosmic hard X-ray background. At MeV energy range, Seyferts having non-thermal electrons in coronae above accretion disks or MeV blazars may explain the background radiation. We propose that future measurements of the angular power spectra of anisotropy of the cosmic X-ray and MeV gamma-ray backgrounds will be key to deciphering these backgrounds and the evolution of active galactic nuclei (AGNs). As AGNs trace the cosmic large-scale structure, spatial clustering of AGNs exists. We show that e-ROSITA will clearly detect the correlation signal of unresolved Seyferts at 0.5-2 keV and 2-10 keV bands and will be able to measure the bias parameter of AGNs at both bands. Once the future hard X-ray all sky satellites achieve the sensitivity better than 10^{-12} erg/cm^2/s at 10-30 keV or 30-50 keV - although this is beyond the sensitivities of current hard X-ray all sky monitors - angular power spectra will allow us to independently investigate the fraction of Compton-thick AGNs in all Seyferts. We also find that the expected angular power spectra of Seyferts and blazars in the MeV range are different by about an order of magnitude, where the Poisson term, so-called shot noise, is dominant. Current and future MeV instruments will clearly disentangle the origin of the MeV gamma-ray background through the angular power spectrum.
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