Write the following function in the simplest form: `tan^(-1)(1/(sqrt(x^2-1))),|x|>1`

Explanation

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

### Step 1: Substitute \( x \) with \( \sec \theta \)
Let \( x = \sec \theta \). This substitution is valid since \( |x| > 1 \) implies that \( \theta \) is in the range where the secant function is defined.

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