Question

Solve for x:

cot^-1(1/(x² - 1)) + tan^-1(x² - 1) = π/2

Answer 1

It is true only when 1/(x² - 1) = x² - 1

⇒ (x² - 1)² = 1

⇒ (x² - 1) = ±1

⇒ x² = 1 ± 1 = 2, 0

⇒ x = 0, ±√2