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Question
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
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Solution
L.H.S. = `sqrt((1 + sinA)/(1 - sinA))`
= `sqrt((1 + sinA)/(1 - sinA) xx (1 + sinA)/(1 + sinA)`
= `sqrt((1 + sinA)^2/(1 - sin^2A))`
= `sqrt((1 + sinA)^2/cos^2A)`
= `(1 + sinA)/cosA`
= `1/cosA + sinA/cosA`
= sec A + tan A = R.H.S.
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