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Prove that tan (2 tan^(-1) x ) = 2 tan...

Prove that ` tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3))`.

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To prove that \( \tan(2 \tan^{-1} x) = 2 \tan(\tan^{-1} x + \tan^{-1} x^3) \), we will start with the left-hand side (LHS) and simplify it step by step. ### Step 1: Start with LHS We have: \[ \text{LHS} = \tan(2 \tan^{-1} x) \] ...
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