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

Explanation

`2 \tan ^{-1} x=\tan ^{-1} (\frac{2 x}{1-x^{2}})`


Replacing `x` with `\frac{1}{2}`


`2 \tan ^{-1} \frac{1}{2}=\tan ^{-1} \frac{2 \times \frac{1}{2}}{1-\ (\frac{1}{2}\)^{2}}`



`\tan ^{-1}(\frac{1}{1-\frac{1}{4}})=\tan ^{-1}(\frac{1}{\frac{4-1}{4}})=\tan ^{-1}(\frac{1}{\frac{3}{4}})`



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