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Question
Prove that `1 + (cot^2 α)/(1 + "cosec" α) = "cosec" α`
Theorem
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Solution
L.H.S. = `1 + (cot^2 α)/(1 + "cosec" α)`
= `1 + ("cosec"^2α - 1)/(1 + "cosec" α)`
= `1 + ((1 + "cosec" α)("cosec" α - 1))/(1 + "cosec" α)`
= 1 + cosec α – 1
= cosec α
= R.H.S.
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