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Question
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Solution
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
LHS = `(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1)`
= `(cosec^2A + cosecA + cosec^2A - cosecA)/(cosec^2A - 1)`
= `(2cosec^2A)/cot^2A(Q cosec^2A - 1 = cot^2A)`
= `(2/sin^2A)/(cos^2A/sin^2A) = 2/cos^2A = 2sec^2A`
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