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