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Question
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
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Solution
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
`cot^2A - 2cotA cosecA + cosec^2x = (1 - cosA)/(1 + cosA)`
`(cos^2A)/(sin^2A) - (2cosA)/(sin^2A) + 1/(sin^2A) = (1 - cosA)/(1 + cosA)`
`(cos^2A - 2cosA + 1)/(sin^2A) = (1 - cosA)/(1 + cosA)`
`(cos^2A - 2cosA + 1)/(1 - cos^2A) = (1 - cosA)/(1 + cosA)`
`((1 - cosA)(1 - cosA))/((1 + cosA)(1 - cosA)) = (1 - cosA)/(1 + cosA)`
`(1 - cosA)/(1 + cosA) = (1 - cosA)/(1 + cosA)`
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