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Question
Prove that:
`1/(1 + sin(90^@ - A)) + 1/(1 - sin(90^@ - A)) = 2sec^2(90^@ - A)`
Solution
`1/(1 + sin(90^@ - A)) + 1/(1 - sin(90^@ - A))`
= `1/(1 + cosA) + 1/(1 - cosA)`
= `(1 - cosA + 1 + cosA)/((1 + cosA)(1 - cosA))`
= `2/(1 - cos^2A)`
= 2 cosec2 A
= 2 sec2 (90° – A)
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