Question

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

`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`

Answer 1

L.H.S 

`cos A/(1 + sin A) + (1 + sin A)/cos A `

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

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

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

= `(1+1+2sinA)/((1+sinA)(cosA))`

= `(2+2sinA)/((1+sinA)(cosA))`

= `(2(1+sinA))/((1+sinA)(cosA))`

= `2/(cosA)`

= 2 secA

= R.H.S