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Question
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Solution
We have to prove `1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
We know that, `sin^2 A + cos^2 A = 1`
So,
`1/(1 + sin A) + 1/(1 - sin A) =((1 - sin A) + (1 + sin A))/((1 + sin A)(1 - sin A))`
`= (1 - sin A + 1+ sin A)/(1 - sin^2 A)`
`= 2/cos^2 A`
`= 2 sec^2 A`
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