Question

If tan^-1 x + 2cot^-1 x = `(5pi)/6`, then x is

Options

• `1/sqrt3`

• `sqrt3`

• 3

• `(sqrt3 - 1)/(sqrt3 + 1)`

Answer 1

`1/sqrt3`

Explanation:

Given, tan^-1 x + 2cot^-1 x = `(5pi)/6`

`=> tan^-1 x + cot^-1 x + cot^-1 x = (5pi)/6`

`=> cot^-1 x = (5pi)/6 - pi/2  ..[because tan^-1 x + cot^-1 x = pi/2]`

`=> cot^-1 x = pi/3`

`=> x = cot  pi/3`

`=> x = 1/sqrt3`