Let, `tan^-1y=tan^-1x+tan^-1((2x)/(1-x^2))`, where `absx lt 1/sqrt3`. Then a value of y is:

Options

A. `(3x -x^(3))/(1 -3x^(2))`
B. `(3x + x^(3))/(1 - 3x^(2))`
C. `(3x -x^(3))/(1 + 3x^(2))`
D. `(3x + x^(3))/(1 + 3x^(2))`

Answer

B

Explanation

`(-1)/(sqrt3) lt x lt (1)/(sqrt3)`
Let `x = tan theta`
`:. (-pi)/(6) lt theta lt (pi)/(6)`
`:. Tan^(-1) y = theta + tan^(-1) tan 2 theta = theta + 2theta = 3 theta`
`:. Y = tan 3 theta = (3 tan theta - tan^(3) theta)/(1-3 tan^(2) theta)`
`:. y = (3x -x^(3))/(1 -3x^(2))`