Question

Prove that : 2 tan^-1 (2x/1 - x^2) = 2 pi/3

Answer 1

2 tan^-1 (2x/1 - x^2) = 2 pi/3

Take x as tan theta

Theta = tan^-1 x

tan^-1(2 tan theta/ 1 - tan^2 theta) = pi/3

tan^-1 (tan 2 theta) = pi/3

2 theta = pi/3

theta = pi/6

tan^-1 x = pi/6

x = tan pi/6

x = 1/root 3

$\rule{200}{2}$

Answer 2

Take x as tan theta

Theta = tan^-1 x

tan^-1(2 tan theta/ 1 - tan^2 theta) = pi/3

tan^-1 (tan 2 theta) = pi/3

2 theta = pi/3

theta = pi/6

tan^-1 x = pi/6

x = tan pi/6

x = 1/root 3