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

Answer

`x=ab`

Explanation

$$ \Rightarrow \cos ^{-1} \frac{\mathrm{a}}{\mathrm{x}}+\cos ^{-1} \frac{1}{\mathrm{a}}=\cos ^{-1} \frac{1}{\mathrm{~b}}+\cos ^{-1} \frac{\mathrm{b}}{\mathrm{x}} $$
We know that,
$$ \cos ^{-1} x+\cos ^{-1} y=\cos ^{-1}\left[x y-\sqrt{1-x^{2}} \sqrt{1-y^{2}}\right] $$
By substituting this formula we get,
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