If , where , then the value of…

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

If tan⁡−1y=tan⁡−1x+tan⁡−1(2x1−x2)\tan^{-1}y=\tan^{-1}x+\tan^{-1}\left(\frac{2x}{1-x^2}\right), where ∣x∣<13|x|<\frac{1}{\sqrt{3}}, then the value of yy is (1) 3x−x31−3x2\frac{3x-x^3}{1-3x^2} (2) 3x+x31−3x2\frac{3x+x^3}{1-3x^2} (3) 3x−x31+3x2\frac{3x-x^3}{1+3x^2} (4) 3x+x31+3x2\frac{3x+x^3}{1+3x^2}

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