The value of `tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))}` is `(sqrt(29))/3` (b) `(29)/3` (c) `(sqrt(3))/(29)` (d) `3/(29)`

Explanation

To find the value of \( \tan\left(\cos^{-1}\left(\frac{1}{5\sqrt{2}}\right) - \sin^{-1}\left(\frac{4}{\sqrt{17}}\right)\right) \), we will follow these steps:

### Step 1: Convert \( \cos^{-1} \) to \( \tan^{-1} \)

Using the identity:
\[ \cos^{-1}(x) = \tan^{-1}\left(\frac{\sqrt{1-x^2}}{x}\right) \]
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