  We investigate the controllability of electromagnetically induced
transparency (EIT) and Fano resonances in hybrid optomechanical system which is
composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside
high-finesse Fabry-P\'erot cavity driven by a single mode optical field along
the cavity axis and a transverse pump field. Here, transverse optical field is
used to control the phenomenon of EIT in the output probe laser field. The
output probe laser field can efficiently be amplified or attenuated depending
on the strength of transverse optical field. Furthermore, we demonstrate the
existence of Fano resonances in the output field spectra and discuss the
controlled behavior of Fano resonances using transverse optical field. To
observe this phenomena in laboratory, we suggest a certain set of experimental
parameters.
