Question

If α ≤ 2 sin^–1x + cos^–1x ≤ β, then ______.

Options

• α = `(-pi)/2`, β = `pi/2`

• α = β = π

• α = `(-pi)/2`, β = `(3pi)/2`

• α = 0, β = 2π

Answer 1

If α ≤ 2 sin^–1x + cos^–1x ≤ β, then α = β = π.

Explanation:

We have `(-pi)/2 ≤ sin^-1x ≤ pi/2`

⇒ `(-pi)/2 + pi/2 ≤ sin^-1x + pi/2 ≤ pi/2 + pi/2`

⇒ 0 ≤ sin^–1x + (sin^–1x + cos^–1x) ≤ π

⇒ 0 ≤ 2sin^–1x + cos^–1x ≤ π