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Question
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
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Solution
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
= `(1 + cosA)/(1 - cosA).(1 + cosA)/(1 + cosA)`
= `((1 + cosA)^2)/(1 - cos^2A) = (1 + cosA)^2/sin^2A`
= `[(1 + cosA)/sinA]^2 = [1/sinA + cosA/sinA]^2`
= `(cosecA + cotA)^2`
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