Question

Solve for x: [sin^-1x] + [cos^-1x] = 0, where x is a non negative real number and [,] denotes the greatest integer function.

Answer 1

Given, [sin^-1x] + [cos^-1x] and x ≥ 0

⇒ [sin^-1x] = 0 and [cos^-1x]  = 0

⇒ x ∈ [0, sin1] & x  ∈ (cos1, 1]

⇒ x ∈ (cos1, sin1)