Write `cot^(-1)(1/(sqrt(x^2-1))),|x|>1`in the simplest form.

Explanation

To simplify the expression \( \cot^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right) \) for \( |x| > 1 \), we can follow these steps:

### Step 1: Substitute \( x \) with \( \sec \theta \)
Let \( x = \sec \theta \). Since \( |x| > 1 \), \( \theta \) will be in the range where \( \sec \theta \) is defined (i.e., \( \theta \) is not equal to \( \frac{\pi}{2} + n\pi \) for any integer \( n \)).

### Step 2: Simplify \( \sqrt{x^2 - 1} \)
Using the identity \( \sec^2 \theta - 1 = \tan^2 \theta \), we have:
\[
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