Abstract

If α, β, and γ are the three angles between a line passing through the origin and the three rectangular co-ordinate axes, then the equation connecting them is as follows:cos2α+cos2β+cos2γ = 1.This is the law of direction-cosines of a line. Substituting (cos 2α+1)/2 for cos2α, &c., we get:cos 2α+cos 2β+cos 2γ = −1.

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