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Question
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Solution
L.H.S. = `secA/(secA + 1) + secA/(secA - 1)`
= `(sec^2A - secA + sec^2A + secA)/(sec^2A - 1`
= `(2sec^2A)/tan^2A` ...(∵ sec2 A – 1 = tan2 A)
= `(2/cos^2A)/(sin^2A/cos^2A)`
= `2/sin^2A`
= 2 cosec2 A = R.H.S.
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