$\"\"$

The function is $\"\"$ .

A function has a inverse if and only if it is a one to one function.

If a trigonometric function is a one to one function, it must be either increasing or decreasing function.

Consider $\"\"$ .

Differentiate with respect to $\"\"$ .

$\"\"$ .

$\"\"$ if $\"\"$ .

So the above function is strictly monotonic and has an inverse for $\"\"$ or $\"\"$ .

$\"\"$

The above function is strictly monotonic and has an inverse for $\"\"$ or $\"\"$ .