Solve the equation: `cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)(1/a)`

Explanation

To solve the equation \( \cos^{-1}\left(\frac{a}{x}\right) - \cos^{-1}\left(\frac{b}{x}\right) = \cos^{-1}\left(\frac{1}{b}\right) - \cos^{-1}\left(\frac{1}{a}\right) \), we can follow these steps:

### Step 1: Rewrite the Equation
We start with the given equation:
\[ \cos^{-1}\left(\frac{a}{x}\right) - \cos^{-1}\left(\frac{b}{x}\right) = \cos^{-1}\left(\frac{1}{b}\right) - \cos^{-1}\left(\frac{1}{a}\right) \]

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