If cos⁡(β−γ)+cos⁡(γ−α)+cos⁡(α−β)=−32\cos(\beta - \gamma) + \cos(\gamma - \alpha) + \cos(\alpha - \beta) = -\frac{3}{2}, p…

Mathematics

Problem

If cos⁡(β−γ)+cos⁡(γ−α)+cos⁡(α−β)=−32\cos(\beta - \gamma) + \cos(\gamma - \alpha) + \cos(\alpha - \beta) = -\frac{3}{2}, prove that cos⁡α+cos⁡β+cos⁡γ=sin⁡α+sin⁡β+sin⁡γ=0.\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0.

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