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: Substitution
Let \( x = \sec(\theta) \). This substitution is valid since \( |x| > 1 \) implies \( \theta \) is in the range where secant is defined.

### Step 2: Rewrite the expression
Using the identity \( \sec^2(\theta) = 1 + \tan^2(\theta) \), we can express \( \sqrt{x^2 - 1} \) as follows:
\[
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