solve the equation: sin^-1 x + cos^-1 x = pi/2 

The equation given is:

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

This equation is a known identity. For any \( x \) in the domain of the inverse sine and inverse cosine functions, the following relationship holds:

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

Thus, the equation is valid for all \( x \) in the domain of the inverse functions, which is \( -1 \leq x \leq 1 \).

So, the solution is:

\[
\boxed{-1 \leq x \leq 1}
\]

This equation is always true as long as \( x \) is within the valid domain of the inverse sine and cosine functions.

Would you like further clarification or have any specific questions?

### Relative Questions:
1. What is the domain of \( \sin^{-1} x \) and \( \cos^{-1} x \)?
2. Can we derive other trigonometric identities similar to this one?
3. How would the equation change if we added a constant to one of the inverse functions?
4. What happens if we equate \( \sin^{-1} x + \cos^{-1} x \) to something other than \( \frac{\pi}{2} \)?
5. How does this identity apply in practical trigonometry problems?

**Tip:** Always check the domain of inverse trigonometric functions when solving related equations.

solve the equation: sin^-1 x + cos^-1 x = pi/2

Learn how to solve the equation sin^-1(x) + cos^-1(x) = pi/2, which utilizes key trigonometric identities. Understand the domain of inverse trigonometric functions and apply this identity for any x within the range -1 ≤ x ≤ 1. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation