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Question
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Solution
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
LHS = `sqrt((1 + sin A)/(1 - sin A)`
Rationalize the numerator abd denominator with `sqrt(1 + sin A)`
LHS = `sqrt(((1 + sin A)(1 + sin A))/((1 - sin A)(1 + sin A)))`
= `sqrt((1 + sin A)^2/(1 - sin^2 A))`
= `sqrt((1 + sin A)^2/(cos^2 A))`
= `(1 + sin A)/(cos A)`
= `1/(cos A) + (sin A)/(cos A)`
= sec A + tan A
= RHS
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