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