Question

If `a + pi/2 < 2tan^-1x + 3cot^-1x < b`, then a and b are respectively.

Options

• `pi/2` and 2π

• `pi/2` and `-pi/2`

• 0 and π

• 0 and 2π

Answer 1

`underline(pi/2 "and"  2π)`

Explanation:

`a + pi/2 < 2tan^-1x + 3cot^-1x < b`

⇒ `a + pi/2<2(tan^-1x + cot^-1x) + cot^-1x < b`

⇒ `a + pi/2 < pi + cot^-1x < b`

⇒ `a - pi/2< cot^-1x<b - pi`

As 0 < cot^-1x < π,

a = `pi/2` and b = 2π