https://file.aiquickdraw.com/mathbot/file/1729362919615do8h8t4s.jpg

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.

Solve the equation: sin^(-1)(x) + cos^(-1)(x) = π/2

Find the solution to the trigonometric equation sin^(-1)(x) + cos^(-1)(x) = π/2. This problem explores the inverse sine and cosine identity, and is suitable for students in Grades 11-12 studying trigonometric functions.

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