Prove that : `tan^(-1)(1/2) + tan^(-1)(1/3) = tan^(-1)(3/5) + tan^(-1)(1/4) = pi/4`

Explanation

To prove that \( \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) = \tan^{-1}\left(\frac{3}{5}\right) + \tan^{-1}\left(\frac{1}{4}\right) = \frac{\pi}{4} \), we will evaluate both expressions step by step.

### Step 1: Evaluate \( x = \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \)

Using the formula for the sum of inverse tangents:
\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]
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