If α + β + γ = 2 π , then the system of equations x + cos γ y + cos β z = 0 cos γ x + y + cos α z = 0 cos β x + cos α y + z = 0 has :

Step-by-step solution

Given, α + β + γ = 2 π Now, Δ = 1 cos γ cos β cos γ 1 cos α cos β cos α 1 By expanding along the first column, we get ∆ = 1 1 - cos 2 α - cos γ cos γ - cos α . cos β + cos β cos α . cos γ - cos β ∆ = 1 - cos 2 α - cos 2 γ + cos γ . cos α . cos β + cos β . cos α . cos γ - cos 2 β = 1 - cos 2 α - cos 2 β - cos 2 γ + 2 cos α . cos β . cos