LHS : cos theta/(1-sin theta)+costheta/(1+sintheta)
=(costheta(1+sintheta)+costheta(1-sintheta))/((1-sintheta)(1+sin theta))->common denominator
=(costheta+sinthetacostheta+costheta-sinthetacostheta)/(1-sin^2theta)
=(costheta+cancel(sinthetacostheta)+costheta-cancel(sinthetacostheta))/(1-sin^2theta)
=(2costheta)/cos^2theta->use the property sin^2theta+cos^2theta=1
=(2cancelcostheta)/cos^cancel2theta
=2/costheta
=RHS