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Question
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
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Solution
L.H.S. = `1/(1 - sinA) + 1/(1 + sinA)`
= `(1 + sinA + 1 - sinA)/((1 - sinA)(1 + sinA))`
= `2/(1 - sin^2A)`
= `2/cos^2A`
= 2 sec2 A = R.H.S.
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