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Question
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Solution
L.H.S. = `sqrt((1 - cosA)/(1 + cosA))`
= `sqrt((1 - cosA)/(1 + cosA) xx (1 - cosA)/(1 - cosA))`
= `sqrt((1 - cosA)^2/(1 - cos^2A))`
= `sqrt((1 - cosA)^2/(sin^2A)`
= `(1 - cosA)/sinA`
= `1/sinA - cosA/sinA`
= cosec A – cot A = R.H.S.
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