Let tan–1y = tan–1x + tan–1 \left(\right. \frac{2 x}{1 - x^{2}} \left.\right), where |x| < \frac{1}{\sqrt{3}} . Then a value of y is:

Engineering

Mathematics

Properties of Inverse Trigonometric Function

Question

Let tan^–1y = tan^–1x + tan^–1 $(\frac{2 x}{1 - x^{2}})$ ,

where |x| < $\frac{1}{\sqrt{3}} .$ Then a value of y is:

$\frac{3 x - x^{3}}{1 + 3 x^{2}}$

$\frac{3 x - x^{3}}{1 - 3 x^{2}}$

$\frac{3 x + x^{3}}{1 + 3 x^{2}}$

$\frac{3 x + x^{3}}{1 - 3 x^{2}}$

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tan^–1 y = 3 tan^–1x = tan^{–1 $(\frac{3 x - x^{3}}{1 - 3 x^{2}}), | X | < \frac{1}{\sqrt{3}}$}

^{$\Rightarrow y = (\frac{3 x - x^{3}}{1 - 3 x^{2}})$}