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Math Help - Trig problem

  1. #1
    Super Member
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    Smile Trig problem

    hi everyone
    Assume that \alpha ,\beta ,\gamma satisfy 0< \alpha < \beta < \gamma < 2\pi if,
    \cos(x+\alpha )+\cos(x+\beta )+\cos(x+\gamma )=0,\forall x \in \mathbb{R}.
    Find \gamma -\alpha
    just hints
    thanks.
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  2. #2
    Senior Member
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    If the relationship is true for all x, it's certainly true for x=-beta, x=-alpha and x=-gamma. Try substituting in these values and what you're looking for will fall out.
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