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Question
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
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Solution
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA))`
= `((sec^2A - tan^2A) + (secA - tanA)^2)/(cosecA(secA - tanA))`
= `((secA - tanA)(secA + tanA) + (secA + tanA)^2)/(cosecA(secA - tanA))`
= `((secA + tanA) + (secA - tanA))/(cosecA)`
= `(2secA)/(cosecA)`
= `2(1/cosA)/(1/sinA)`
= 2 tanA
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