Question

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`

Answer 1

L.H.S

= `sqrt((1+sinA)/(1-sinA))`

= `sqrt(((1+sinA)(1+sinA))/((1-sinA)(1+sinA))`

= `(1+sinA)/(sqrt(1-sin^2A))`

= `(1+sinA)/sqrt(cos^2A)`

= `(1+sinA)/cosA`

= secA + tan A

= `1/cos A + sin A/cos A`

= R.H.S