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Question
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Solution
LHS = `(cosecA - sinA)(secA - cosA)(tanA + cotA)`
= `(1/sinA -sinA)(1/cosA - cosA)(tanA + 1/tanA)`
= `((1-sin^2A)/sinA)((1 - cos^2A)/cosA)(sinA/cosA + cosA/sinA)`
= `(cos^2A/sinA)(sin^2A/cosA)((sin^2A + cos^2A)/(sinA.cosA))`
= 1
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