Find the maximum and minimum values of `(sin^(-1)x)^3+(cos^(-1)x)^3,` where `-1lt=xlt=1.`

Explanation

To find the maximum and minimum values of the expression \( (\sin^{-1} x)^3 + (\cos^{-1} x)^3 \) for \( -1 < x < 1 \), we can use the identity for the sum of cubes and some properties of inverse trigonometric functions.

### Step-by-Step Solution:

1. **Use the Identity for Sum of Cubes:**
We know that:
\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
...