Question

If 3 tan^–1x + cot^–1x = π, then x equals ______.

Options

• 0

• 1

• – 1

• `1/2`

Answer 1

If 3 tan^–1x + cot^–1x = π, then x equals 1.

Explanation:

Given that 3 tan^–1x + cot^–1x = π

⇒ 2 tan^–1x + tan^–1x + cot^–1x = π

⇒ `2 tan^-1x + pi/2` = π  ......`[because tan^-1x + cot^-1x = pi/2]`

⇒ `2tan^-1x = pi - pi/2`

⇒ `2tan^-1x = pi/2`

⇒ `2tan^-1x = pi/4`

⇒ `tan^-1x = tan^-1(1)`

⇒ x = 1