Question

If cos^–1 x > sin^–1 x, then ______.

Options

• `1/sqrt(2) < x ≤ 1`

• `0 ≤ x ≤ 1/sqrt(2)`

• `-1 ≤ x < 1/sqrt(2)`

• x > 0

Answer 1

If cos^–1 x > sin^–1 x, then `underlinebb(-1 ≤ x < 1/sqrt(2))`.

Explanation:

cos^–1 x > sin^–1 x [where x ∈ [–1, 1]]

∵ cos^–1 x = `π/2 - sin^-1 x`

∴ `π/2 - sin^-1 x > sin^-1 x`

`\implies 2 sin^-1 x < π/2` 

`\implies sin^-1 x < π/2`

`\implies x < 1/sqrt(2)`

∵ –1 ≤ x ≤ 1

`-1 ≤ x < 1/sqrt(2)`