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Question
Prove the following identities:
`1 + (cot^2θ)/(1 + "cosec" θ) = "cosec" θ`
Theorem
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Solution
We know that cot2θ = (cosec2θ – 1).
∴ LHS = `1 + (("cosec"^2θ - 1))/(("cosec" θ + 1))`
= 1 + (cosec θ – 1)
= cosec θ = RHS
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