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

Explanation

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

### Step 1: Substitute \( x \) with \( a \sin \theta \)
Let \( x = a \sin \theta \). This substitution is useful because it relates \( x \) to a trigonometric function, which will help simplify the expression involving \( \sqrt{a^2 - x^2} \).

### Step 2: Rewrite the expression
Substituting \( x = a \sin \theta \) into the expression gives:
\[
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