Question

If `tan^-1x = pi/10` for some x ∈ R, then the value of cot^–1x is ______.

Options

• `pi/5`

• `(2pi)/5`

• `(3pi)/5`

• `(4pi)/5`

Answer 1

If `tan^-1x = pi/10` for some x ∈ R, then the value of cot^–1x is `(2pi)/5`.

Explanation:

We know tan^–1x + cot^–1x = `pi/2`.

Therefore cot^–1x = `pi/2 - pi/10`

⇒ cot^–1x = `pi/2 - pi/10 = (2pi)/5`.