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