Question

If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.

Options

• 1

• `1/2`

• 0

• –1

Answer 1

If `3tan^-1x +cot^-1x = pi`, then xis equal to 1.

Explanation:

`3tan^-1x +cot^-1x = pi`

⇒ `2tan^-1x + tan^-1x + cot^-1x = pi`

⇒ `2tan^-1x + pi/2` = π

⇒ `tan^-1x = pi/4`

⇒ `tan(tan^-1x) = tan  pi/4`

⇒ x = 1