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

Prove that `tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/(sqrt(3))`

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To prove that \[ \tan^{-1} x + \tan^{-1} \left( \frac{2x}{1 - x^2} \right) = \tan^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right), \quad |x| < \frac{1}{\sqrt{3}}, \] we will use the formula for the sum of inverse tangents: ...
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