If and 1 4 ( + - ) 1 4 ( + - ) 1 4 ( + - ) = 1

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

If α+β+γ=π\alpha + \beta + \gamma = \pi andtan⁡14(β+γ−α)tan⁡14(γ+α−β)tan⁡14(α+β−γ)=1,\tan \frac{1}{4}(\beta + \gamma - \alpha) \tan \frac{1}{4}(\gamma + \alpha - \beta) \tan \frac{1}{4}(\alpha + \beta - \gamma) = 1,then prove that 1+cos⁡α+cos⁡β+cos⁡γ=01 + \cos \alpha + \cos \beta + \cos \gamma = 0.

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