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