Question

How can i find the Domain?

`f(x)=sqrt((1+sinx)/(1-sinx))`

Answer 1

The only concern is to avoid division by 0

Explanation:

When a radical is present, one instinctively thinks that the domain will depend upon conditions where the expression under the radical is negative and avoid those conditions.

To check for negatives, we will let the sine function become -1 and 1:

Let sin(x) = -1:

`(1-1)/(1- -1)= 0/2 = 0`

Let sin(x) = 1:

`(1+1)/(1- 1) = 2/0 = "undefined"`

Please observe that neither the numerator nor the denominator can become negative but division by 0 can occur, therefore, we must restrict the domain to prevent this:

`1 -sin(x)!=0`

`sin(x)!=1`

`x !=sin^-1(1)`

The primary value is:

`x = pi/2`

This condition repeats at integer multiples of `2pi`L

`x != pi/2+2npi; n in ZZ`