Prove each of the following identities:

Consider L.H.S. =

Multiply and divide by (1 + cos θ) in first part and (1 – cos θ) in the second part:

=

=

=

= [(1 + cos θ)/sin θ] + [(1 – cos θ)/sin θ]

= [(1/sin θ) + (cos θ/sin θ)] + [(1/sin θ) – (cos θ/sin θ)]

= [cosec θ + cot θ] + [cosec θ – cot θ]

= 2 cosec θ

= R.H.S.

Hence, proved.