Evaluate (1 + sin x) / (1-sin x)

Answer:

(1+sin x) /(1-sinx)

We shall multiply and divide the above equation using [1 + sinx].

As a result, we receive the solution as

(1 + sinx) (1 + sinx) / (1 – sinx) (1 + sinx)

(1 – sinx) (1 + sinx) can be expressed as (1 – sin²x) using the identity (a-b) (a+b) = (a²-b²)

=(1 + sinx)² / (1 – sin²x)

We know that sin²x + cos²x = 1 so 1 – cos²x= sin²x

=(1 + sinx)²/ cos2x

= { (1 + sinx) / cos x} ²

= {sec x + tan x }²

 1+sin /1-sinx ={sec x + tan x }²