  We report results obtained from the optical and X-ray studies of the Be/X-ray
binary 1A 0535+262/HD 245770 during the 2020 October giant X-ray outburst,
using the 1.2 m telescope at Mount Abu Infrared observatory and AstroSat,
respectively. The peak flux of the outburst was recorded to be around 11 Crab
in the 15-50 keV range, the highest ever observed from the pulsar. We performed
optical observations in the 6000-7200 angstroms band before, during, and after
the outburst to investigate the evolution of the circumstellar disc of the Be
star between 2020 February and 2022 February. Our optical spectra exhibit
prominent emission lines at 6563 angstroms (H I), 6678 angstroms (He I), and
7065 angstroms (He I). We found a significantly variable Halpha line in the
spectra. The single-peaked line profile appeared asymmetric with broad red- &
blue-wings in the data before and during the outburst. The post-outburst
observations, however, resulted in a double-peaked profile with asymmetry in
the blue-wing. Our observations before the outburst confirmed a larger Be disc
that decreased in size as the outburst progressed. Furthermore, the observed
variabilities in the Halpha line profile and parameters suggest the presence of
a highly misaligned, precessing, and warped Be disc. AstroSat observation of
the pulsar detected pulsations at around 103.55 s in the light curve up to 110
keV. We found strongly energy-dependent pulse profiles with increasing
contribution of the pulsing component in hard X-rays. The broadband spectral
fitting in the 0.7-90.0 keV range confirmed the presence of the known cyclotron
resonance scattering feature at around 46.3 keV.
