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Question
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Solution
LHS = `( tan A + sec A - 1)/(tan A - sec A + 1)`
= `(( tan A + sec A) - (sec^2 A - tan^2 A))/((tan A - sec A) + 1)`
= `(( tan A + sec A)( 1 - sec A + tan A))/(tan A - sec A + 1)`
= tan A + sec A
= `sin A/cos A + 1/cos A = (1 + sin A)/cos A`
= RHS
Hence proved.
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