Trigonometric identity: |

Expanding (1 + cos θ)

^{2},

Applying identity sin

^{2}θ + cos

^{2}θ = 1,

Adding 1 and 1,

Factoring out 2,

Cancel common 1 + cos θ present in numerator and denominator,

Applying identity cosec θ = 1 / sin θ,

= 2 cosec θ... which is the right hand side expression.

Trigonometric identities applied:

- sin2 θ+ cos2 θ = 1
- cosec θ = 1 / sin θ