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Question
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
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Solution
L.H.S. = `(cosecA-1)/(cosecA+1)`
= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`
= `(cosec^2A - 1)/(cosecA + 1)^2`
= `cot^2A/(cosecA + 1)^2`
= `(cos^2A/sin^2A)/(1/sinA + 1)^2`
= `(cosA/(1 + sinA))^2` = RHS.
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