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:

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