Find `tan^(-1). (x)/(sqrt(a^(2) - x^(2)))` in terms of `sin^(-1)`, where `x in (0, a)`

Explanation

To find \( \tan^{-1} \left( \frac{x}{\sqrt{a^2 - x^2}} \right) \) in terms of \( \sin^{-1} \), where \( x \in (0, a) \), we can follow these steps:

### Step 1: Substitute \( x \) with \( a \sin \theta \)
Let us set \( x = a \sin \theta \). This substitution is useful because it relates \( x \) to a sine function, which will help us express everything in terms of \( \sin^{-1} \).

### Step 2: Rewrite the expression
Now, substituting \( x \) into the expression, we have:
\[
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