A line makes an angle alpha, beta, gamma and delta with the diagonals of a cube, prove that cos^2alpha + cos^2beta + cos^2gamma + cos^2delta =4/3

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A line makes angles $α, β, γ, δ$ with the four diagonals of a cube, prove that

${cos}^{2} α + {cos}^{2} β + {cos}^{2} γ + {cos}^{2} δ = \frac{4}{3}$

l

α, β, γ, δ

{cos}^{2} α + {cos}^{2} β + {cos}^{2} γ + {cos}^{2} δ = \frac{4}{3}

α, β, γ

δ

{cos}^{2} α + {cos}^{2} β + {cos}^{2} γ + {cos}^{2} δ = \frac{a}{b}

a

b

a + b

α, β, γ

δ

c o s^{2} α + c o s^{2} β + c o s^{2} γ + c o s^{2} δ = \frac{4}{3}

α, β, γ, δ

{cos}^{2} α + {cos}^{2} β + {cos}^{2} γ + {cos}^{2} δ = ?

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