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Question
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
Solution
`cosA/(1+sinA)+tanA`
= `cosA/(1 + sinA) + sinA/cosA`
= `(cos^2A + sinA + sin^2A)/((1 + sinA)cosA)`
= `(1 + sinA)/((1 + sinA)cosA)`
= `(cos^3A + cosA sinA - sin^2A)/(cos^2A - sinAcosA)`
= `1/cosA`
= sec A
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