Show that 1 cos - - - cos- - - cos- - - 1 cos- - - cos- - - cos - - - 1 -

L.H.S = 1 amp; cos(β α ) amp; cos(γ α ) cos(α β ) amp; 1 amp; cos(γ β ) cos(α γ ) amp; cos(β γ ) amp; 1 ...

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Equality of Matrices

Show that 1...

Question

Show that $∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ =$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & cos (β - α) & cos (γ - α) cos (α - β) & 1 & (cos γ - β) cos (α - γ) & cos (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β, γ

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β, γ

△ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & cos (β - α) & cos (γ - α) cos (α - β) & 1 & cos (γ - β) cos (α - γ) & cos (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β

γ

A = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & cos (β - α) & cos (γ - α) cos (α - β) & 1 & cos (γ - β) cos (α - γ) & cos (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

{cos}^{2} (β - γ) + {cos}^{2} (γ - α) + {cos}^{2} (α - β) = 1 + 2 cos (β - α) cos (γ - α) cos (α - β)

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