Question

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

• A. \( \frac{\pi}{2} \)
• B. \( \pi \)
• C. \( \frac{\pi}{4} \)
• D. \( \frac{3\pi}{4} \)

Hint:

When the sum of inverse sine functions is \( \frac{\pi}{2} \), the sum of the corresponding inverse cosine functions is also \( \frac{\pi}{2} \).

Answer 1

The Correct Option is A

Step 1: Using the identity.
Given that \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), we know that \( \cos^{-1} x + \cos^{-1} y \) must also equal \( \frac{\pi}{2} \) due to complementary angle properties.

Step 2: Conclusion.
Thus, the correct answer is option (A).

Final Answer: \[ \boxed{\text{(A) } \frac{\pi}{2}} \]