# Prove that LHS=RHS

LHS = (cosA-sinA)+1/[(cosA+sinA)-1]

Now, on taking conjugate, we get,

= (cosA-sinA)+1/[(cosA+sinA)-1] * [(cosA+sinA)+1/(cosA+sinA)+1]

Now, on multiplying, we get,

=cos2A-sin2A+2cosA+1/2sinAcosA

=cos2A-sin2A+2cosA+sin2A+cos2A/2sinAcosA

On solving, we get,

=2cos2A+2cosA/2sinAcosA

=cosA+cos2A/sinAcosA

=cosA/sinAcosA +cos2A/sinAcosA

=cosecA+cotA

=R.H.S