If - - - are real numbers- then - -1 cos - cos- - cos- - 1 cos- - cos- - cos - - 1

Δ = cos α amp; sin α amp; 0 cos β amp; sin β amp; 0 cos γ amp; sin γ amp; 0 × cos α amp; sin α amp; 0 cos β amp; sin β amp; 0 cos γ ...

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Properties of Determinants

If α, β, γ ar...

Question

If $α, β, γ$ are real numbers, then $Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s (β - α) & c o s (γ - α) c o s (α - β) & 1 & c o s (γ - β) c o s (α - γ) & c o s (β - γ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$

-1

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c o s α c o s β c o s γ

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c o s α + c o s β + c o s γ

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None of these

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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} ∣ ∣ ∣ ∣ ∣

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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} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣ ∣ =

∣ ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣ ∣

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A = ⎡ ⎢ ⎣ \begin{matrix} 1 & cos (α - β) & cos (α - γ) cos (β - α) & 1 & cos (β - γ) cos (γ - α) & cos (γ - β) & 1 \end{matrix} ⎤ ⎥ ⎦

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