Prove that: `2tan^(-1) {1/2}+tan^(-1) {1/7}=tan^(-1) {(31)/(17)}`

Explanation

To prove that \( 2\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{7}\right) = \tan^{-1}\left(\frac{31}{17}\right) \), we will follow these steps:

### Step 1: Use the double angle formula for inverse tangent
We start with the left-hand side (LHS):
\[ 2\tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{7}\right) \]
Using the identity \( 2\tan^{-1}(x) = \tan^{-1}\left(\frac{2x}{1-x^2}\right) \), we set \( x = \frac{1}{2} \):
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