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Trigonometric identities - 10

Trigonometric identity: 
The LHS expressions contains two rational expressions. Adding these rational expressions together,
Expanding (1 + cos θ)2,

Applying identity sin2 θ + cos2 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: