Question

If \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \), then \( x \) is:

• A. \( \frac{\pi}{3} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{\pi}{3} \)
• D. \( \frac{1}{2} \)

Hint:

The identity \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \) holds for all values in the domain of the inverse trigonometric functions.

Answer 1

The Correct Option is D

Step 1: Using the identity for inverse trigonometric functions. 
We know that: \[ \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \] This identity holds for all values of \( x \). 
Step 2: Conclusion. 
Thus, the value of \( x \) is \( \frac{1}{2} \).