Question

Prove the following trigonometric identity:

`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`

Answer 1

`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