Prove that `tan^(-1)(x/sqrt(a^(2)-x^(2)))=sin^(-1)x/a.`

Explanation

To prove that \( \tan^{-1}\left(\frac{x}{\sqrt{a^2 - x^2}}\right) = \sin^{-1}\left(\frac{x}{a}\right) \), we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

### Step 1: Start with the LHS
The left-hand side is:
\[ LHS = \tan^{-1}\left(\frac{x}{\sqrt{a^2 - x^2}}\right) \]

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