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Equivalence Relation

what is alpha...

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what is alpha , beta , gamma and theta?

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{cos}^{3} (α + θ) {sin}^{3} (β - γ) + {cos}^{3} (β + θ) {sin}^{3} (γ - α) + {cos}^{3} (γ + θ) {sin}^{3} (α - β)

= 3 cos (α + θ) cos (β + θ) cos (γ + θ) \times sin (α - β) sin (β - γ) sin (γ - α)

cos (α + β) sin (γ + θ) = cos (α - β) sin (γ - θ)

tan θ = tan α tan β tan γ

α, β, γ, θ ϵ R

A_{θ} (α, β, γ) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (α + θ) & sin (α + θ) & 1 cos (β + θ) & sin (β + θ) & 1 cos (γ + θ) & sin (γ + θ) & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

α, β, γ

are fixed. then

y = A_{x} (α, β, γ)

α + β + γ = 2 θ

cos θ + cos (θ - α) + cos (θ - β) + cos (θ - γ)

cos (α + β) sin (γ + θ) = cos (α - β) sin (γ - θ)

tan θ - tan α tan β tan γ

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Equivalence Relation

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