Question

The equation tan^–1x – cot^–1x = `(1/sqrt(3))` has ______.

Options

• No solution

• Unique solution

• Infinite number of solutions

• Two solutions

Answer 1

The equation tan^–1x – cot^–1x = `(1/sqrt(3))` has unique solution.

Explanation:

We have tan^–1x – cot^–1x = `pi/6` and tan^–1x + cot^–1x = `pi/2`

Adding them, we get 2tan^–1x = `(2pi)/3`

⇒ tan^–1x = `pi/3`

i.e., x = `sqrt(3)`.