`2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1},` is equal to `(2x)/(1-x^2)` `t(2tan^(-1)x)` `tan(cot^(-1)(-x)-cot^(-1)(x))` `"tan"(2cot^(-1)x)`

Explanation

To solve the problem \( 2 \tan(\tan^{-1}(x) + \tan^{-1}(x^3)) \) where \( x \in \mathbb{R} \setminus \{-1, 1\} \), we will follow these steps:

### Step 1: Let \( \tan^{-1}(x) = \alpha \) and \( \tan^{-1}(x^3) = \beta \)
This means:
\[ x = \tan(\alpha) \quad \text{and} \quad x^3 = \tan(\beta) \]

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