Write each of the following in the simplest form: `cot^(-1){a/(sqrt(x^2-a^2))},|x|> a`

Explanation

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

### Step-by-Step Solution:

1. **Substitution**: Let \( x = a \csc \theta \). This substitution is useful because it relates \( x \) to a trigonometric function, which will help simplify the expression.

\[
\text{Let } x = a \csc \theta
...