Let –1 –1 –1 2 2x tan y tan x tan 1 x æ ö = + ç ÷ è ø – , where or 1 x 3 < . Then a value of y is :

Question:

Let

$$\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)$$

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

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

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

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

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

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2015

Solution:

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