To solve the equation \( 2 \sin^{-1}(x) = \frac{\pi}{2} \), follow these steps:

1. **Divide both sides by 2** to isolate \( \sin^{-1}(x) \):
   \[
   \sin^{-1}(x) = \frac{\pi}{4}
   \]

2. **Apply the sine function** to both sides to eliminate the inverse sine:
   \[
   x = \sin\left(\frac{\pi}{4}\right)
   \]

3. **Evaluate** \( \sin\left(\frac{\pi}{4}\right) \). We know:
   \[
   \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}
   \]

Thus, the solution is:
\[
x = \frac{\sqrt{2}}{2}
\]

### Final Answer:
\[
x = \frac{\sqrt{2}}{2}
\]

Would you like further clarification or a more detailed explanation?

### 5 Related Questions:
1. What is the range of the inverse sine function?
2. How would the solution change if the equation were \( 3 \sin^{-1}(x) = \frac{\pi}{2} \)?
3. How does the sine function behave in different quadrants of the unit circle?
4. Can you solve \( \sin^{-1}(x) = \frac{\pi}{6} \)?
5. How would you solve \( 2 \cos^{-1}(x) = \frac{\pi}{2} \)?

### Tip:
When solving equations involving inverse trigonometric functions, always check that the solution lies within the defined range of the inverse function.

This page provides a detailed step-by-step solution to solve the equation 2sin⁻¹(x) = π/2. Learn how to isolate sin⁻¹(x), apply the sine function, and evaluate the sine of π/4 to find x = √2/2. Suitable for students in Grades 10-12 studying trigonometry and inverse trigonometric functions.

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