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