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Question
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Solution
LHS = `(secA - 1)/(secA + 1)`
= `(1/cosA - 1)/(1/cosA + 1) = (1 - cosA)/(1 + cosA)`
= `(1 - cosA)/(1 + cosA) xx (1 + cosA)/(1 + cosA)`
= `(1-cos^2A)/(1 + cosA)^2`
= `sin^2A/(1 + cosA)^2` (∵ `1 - cos^2A = sin^2A`)
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