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