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Trigonometry

Source: 2005 National High School Mathematics League, Exam One, Problem 9

March 19, 2020
trigonometry

Problem Statement

If 0<α<β<γ<2π0<\alpha<\beta<\gamma<2\pi, for all x∈Rx\in\mathbb{R}, cos⁡(x+α)+cos⁡(x+β)+cos⁡(x+γ)=0\cos(x+\alpha)+\cos(x+\beta)+\cos(x+\gamma)=0, then γ−α=\gamma-\alpha=________.
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