Question

The value of the determinant `|(1, cos(β - α), cos(γ - α)),(cos(α - β), 1, cos(γ - β)),(cos(α - γ), cos(β - γ), 1)|` is equal to ______.

Options

• cosα + cosβ + cosγ

• cosα cosβ + cosβ cosγ + cosγ cosα

• –1

• 0

Answer 1

The value of the determinant `|(1, cos(β - α), cos(γ - α)),(cos(α - β), 1, cos(γ - β)),(cos(α - γ), cos(β - γ), 1)|` is equal to 0.

Explanation:

Δ = `|(1, cos(β - α), cos(γ - α)),(cos(α - β), 1, cos(γ - β)),(cos(α - γ), cos(β - γ), 1)|`

The above determinant is obtained by multiplying two zero determinants:

Δ = `|(cosα, sinα, 0),(cosβ, sinβ, 0),(cosγ, sinγ, 0)||(cosα, sinα, 0),(cosβ, sinβ, 0),(cosγ, sinγ, 0)|` = 0

∴ Δ = 0