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