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