We are given the equation $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ and asked to find the value of $x$.

1. Problem Description

We are given the equation $\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$ and asked to find the value of $x$.

2. Solution Steps

The identity that relates the inverse sine and inverse cosine functions is:

$$\sin^{-1} x + \cos^{-1} x = \frac{\pi}{2}$$

This identity holds true for all $x$ in the domain of both $\sin^{-1} x$ and $\cos^{-1} x$, which is $[-1, 1]$.

Since the equation given in the problem is the same as the identity, any $x$ value in the interval $[-1, 1]$ will satisfy the equation.

3. Final Answer

The solution is any $x$ in the interval $[-1, 1]$.

$x \in [-1, 1]$