Prove That: (1 + Cot^2 θ/(1 + Cosec θ)) = Cosec θ - Mathematics

Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.

Sum

LHS = `(1 + cot^2 θ/(1 + cosec θ))`

= `(1 + cosec θ + cosec^2 θ - 1)/(1 + cosec θ)`

= `(cosec θ(1 + cosec θ))/(1 + cosec θ)`

= cosec θ

= RHS
Hence proved.

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