Find the minimum value of `(sec^(-1) x)^(2) + (cosec^(-1) x)^(2)`

Explanation

To find the minimum value of the expression \( (sec^{-1} x)^2 + (cosec^{-1} x)^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Let \( y = sec^{-1} x \)**:
We can denote \( y = sec^{-1} x \). Then, using the identity for cosecant, we have:
\[
cosec^{-1} x = \frac{\pi}{2} - sec^{-1} x = \frac{\pi}{2} - y
...