If `sec^(-1) x = cosec^(-1) y`, then find the value of `cos^(-1).(1)/(x) + cos^(-1).(1)/(y)`

Options

A. π
B. π/4
C. π/2
D. -π/2

Explanation

To solve the problem, we start with the given equation:

**Step 1:** Given that \( \sec^{-1} x = \csc^{-1} y \).

**Step 2:** We know that the range of \( \sec^{-1} x \) is \( [0, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \pi] \) and the range of \( \csc^{-1} y \) is \( [-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}] \). The common value in these ranges is \( \frac{\pi}{4} \).

**Step 3:** Therefore, we can set:
\[
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