Question

Tan inverse 2x/1-x square+cot inverse 1-x square/2x=2pi/3

Answer 1

In the attachment I have answered this problem.

The following results I have applied to solve :

1. Cot^-1(x) = tan^-1(1/x)

2. tan 2A = 2tanA / 1-tan^2A

3. tan^-1 (tanx) = x

See the attachment for detailed solution .

Answer 2

Answer:

$x = 1/\sqrt3$

Step-by-step explanation:

The inverse of tan is cot, if tan is changed to cot then the $\Theta$

value changes upside down. Therefor,

$tan^{-1} (2x/1 - x^2) + tan^{-1}(2x/1 -x^2) = 2\pi/3$

⇒ 2 tan inverse (2x/1 - x^2) = 2pi/3

take x = tan Ɵ and  Ɵ = tan inverse x

⇒ $tan^{-1} (2 tan\Theta/1 -tan^2 \Theta) = \pi/3$

⇒ $tan^{-!} (tan 2\Theta) = \pi/3$

⇒ $2\Theta = \pi/3$

⇒ $\Theta = \pi/6$

⇒ $tan^{-1}x = \pi/6$

⇒ $x = tan \pi/6$  

⇒ $x = 1/\sqrt3$