Find the domain of the inverse trigonometric function is,

Question

Question

Answer 1

Concept:

The domain of inverse sine function, sin x is

Calculation:

The domain of the function is calculated as follows:

⇒ ...(1)

Also,

Square it to get x,

Now,

and

Here we have to find the common values of x.

For,

Here, the values of x for which LHS will change its sign will be -1 and 1 so the values of x for the above inequality,

⇒ ....(2)

For,

....(3)

Take, all the common intervals from equations 1, 2, and 3,

We will get,