Evaluate 1 + sin x /1-sin x

Trignometric ratios is the study of the relation between the sides and angles of a right-angled triangle.

Answer:  (1+sinx) /(1-sinx) =(sec x + tan x )²

Let see, how we can solve

Explanation:

To evaluate:  (1+sin) /(1-sinx)

We will multiply and divide the expression ( 1+sin) /(1-sinx) by (1 + sinx)

Thus, we get

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

=(1 + sinx)² /(1 - sin²x) ------------- (1)                           ( By using identity (a-b) (a+b) = (a²-b²))

As we know that, 

sin²x + cos²x = 1 

So, we can write it as 

 1 – sin²x  =  cos²x

Replacing the denominator of (1) we get,

= (1 + sin x)² / cos²x

= ( (1 + sin x) / cos x) ²

= ( 1/cos x + sin x/cos x)²

We know that, 1/cosx = sec x and sin x/cos x = tan x

Thus, we have

= (sec x + tan x )²                                  

Thus, 1 + sin x /1-sin x=  (sec x + tan x )²