Question

 

 

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

`(1+ secA)/sec A = (sin^2A)/(1-cosA)` 

[Hint : Simplify LHS and RHS separately.]

 

 

Answer 1

 

 L.H.S

`(1+secA)/secA = (1+1/(cosA))/(1/cosA)`

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

= `(cosA+1)`

= `((1-cosA)(1+cosA))/(1-cosA)`

= `(1-cos^2A)/(1-cosA)`

= `(sin^2A)/(1-cosA)`           ...[∵ 1cos² A = sin²A]

R.H.S