Find the value of `2 cos^(-1).(3)/(sqrt13) + cot^(-1).(16)/(63) + (1)/(2) cos^(-1).(7)/(25)`

Explanation

To solve the problem, we need to evaluate the expression:

\[ f = 2 \cos^{-1}\left(\frac{3}{\sqrt{13}}\right) + \cot^{-1}\left(\frac{16}{63}\right) + \frac{1}{2} \cos^{-1}\left(\frac{7}{25}\right) \]

### Step 1: Rewrite the expression using inverse tangent
We can use the identity that relates inverse cosine and inverse tangent. Specifically, we can express \(2 \cos^{-1}(x)\) in terms of \( \tan^{-1} \):

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