Prove that `2tan^(-1)(1/2)+tan^(-1)(1/7)=sin^(-1)((31)/(25sqrt(2)))`

Explanation

To prove that \( 2\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{7}\right) = \sin^{-1}\left(\frac{31}{25\sqrt{2}}\right) \), we will follow these steps:

### Step 1: Rewrite the Left-Hand Side
We start with the left-hand side:
\[ LHS = 2\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{7}\right) \]
We can express \( 2\tan^{-1}\left(\frac{1}{2}\right) \) as:
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