Question

Solve the following inequalities:

4Cot^-1x - (cot^-1X)² - 3 ≥ 0

Answer 1

Given, 4Cot^-1x - (cot^-1X)² - 3 ≥ 0

⇒ 4a - a² - 3 ≥ 0, a = cot^-1x

⇒ a² - 4a + 3 ≤ 0

⇒ (a - 1)(a - 3) ≤ 0

⇒ 1 ≤ a ≤ 3

⇒ 1 ≤ cot^-1 ≤ x ≤ 3

⇒ cot(3) ≤ x ≤ cot(1)