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Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)...

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

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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 use the formula for the addition of inverse tangent functions. ### Step 1: Use the double angle formula for tangent We know that: \[ 2\tan^{-1}(x) = \tan^{-1}\left(\frac{2x}{1-x^2}\right) \] Let \( x = \frac{1}{2} \): ...
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