LHS=(csc θ + sec θ) / (1+ tanθ)
=(1/sintheta + 1/costheta) / (1+sintheta/costheta)
=((sintheta +costheta)/(sinthetacostheta)) / ((costheta+sintheta)/costheta)
=(cancel(sintheta +costheta)/(sinthetacostheta)) xx(costheta/cancel(costheta+sintheta))
=1/sintheta=csctheta=RHS
Proved