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