Question

If \(\sec^{-1}x = \csc^{-1}y\), then \(\cos^{-1}(1/x) + \cos^{-1}(1/y)\) is equal to

• A. \(\pi\)
• B. \(\pi/4\)
• C. \(-\pi/2\)
• D. \(\pi/2\)

Hint:

\(\sin^{-1}\theta + \cos^{-1}\theta = \pi/2\) for \(\theta \in [-1, 1]\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
\(\sec^{-1}x = \cos^{-1}(1/x)\), \(\csc^{-1}y = \sin^{-1}(1/y)\).
Step 2: Detailed Explanation:
\(\cos^{-1}(1/x) = \sin^{-1}(1/y)\)
Add \(\cos^{-1}(1/y)\) both sides:
\(\cos^{-1}(1/x) + \cos^{-1}(1/y) = \sin^{-1}(1/y) + \cos^{-1}(1/y) = \pi/2\)
Step 3: Final Answer:
\(\pi/2\).