We study the azimuthal distributions of Cherenkov photons in Extensive Air Showers (EASs) initiated by $gamma$-ray, proton and iron primaries of different energies incident at various zenith angles over a high altitude observation level. The azimuthal distributions of electrons and positrons along with their asymmetric behaviour have also been studied here to understand the feature of azimuthal distributions of Cherenkov photons in EASs. The main motivation behind this study is to see whether the azimuthal distribution of Cherenkov photons can provide any means to distinguish the $gamma$-ray initiated showers from that of hadron initiated showers in the ground based $gamma$-ray astronomy experiment. Apart from this, such study is also important to understand the natures of $gamma$-ray and hadronic showers in general. We have used the CORSIKA 6.990 simulation package for generating the showers. The study shows the double peak nature of the azimuthal distribution of Cherenkov photons which is due to the separation of electron and positrons in the azimuthal plane. The pattern of distribution is more sensitive for the energy of the primary particle than its angle of incidence. There is no significant difference between distributions for $gamma$-ray and handron initiated showers.
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