The equation given is:

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

This is actually a standard identity in trigonometry:

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

This identity holds true for all $x$ in the domain of $\sin^{-1}(x)$ and $\cos^{-1}(x)$, which is $x \in [-1, 1]$. Therefore, the equation is valid for all $x$ within this range. Thus, the solution to the equation is:

$x \in [-1, 1]$

Let me know if you want more details or have questions!

5 Related Questions:

1. What are the domains of the inverse sine and inverse cosine functions?
2. How can you prove that $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$?
3. What other trigonometric identities involve inverse functions?
4. How would you solve similar equations that involve inverse trigonometric functions?
5. Can this equation be generalized to other trigonometric functions?

Tip:

Always remember that inverse trigonometric functions are only defined within certain domains, so when solving equations involving them, check the domain first.