Inverse Trigonometric Functions

Given two angles are
and Let third angle be
then,

Given that,
and are in AP, then

We have,





but given,

We have Now For Hence, it is a increasing function at at

Range of

We are given the function , which is the inverse sine function.
Step 1: Understanding the domain of
The inverse sine function, , is defined for values of between and , inclusive.
This is because the sine function has a range of .
Step 2: Conclusion
Thus, the domain of the function is , which corresponds to option (b).