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MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

2tan⁡(tan⁡−1x+tan⁡−1x3)2\tan\left(\tan^{-1}x+\tan^{-1}x^3\right), where x∈R∖{−1,1}x\in\mathbb{R}\setminus\{-1,1\}, is equal to (1) 2x1−x2\frac{2x}{1-x^2} (2) tan⁡(2tan⁡−1x)\tan\left(2\tan^{-1}x\right) (3) tan⁡(cot⁡−1(−x)−cot⁡−1x)\tan\left(\cot^{-1}(-x)-\cot^{-1}x\right) (4) tan⁡(2cot⁡−1x)\tan\left(2\cot^{-1}x\right)

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