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Math Help - minimum value

  1. #1
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    minimum value

    Find the minimum value of expression:
    |cos a|+|cos b|+|cos c|+|cos(a-b)|+|cos(b-c)|+|cos(c-a)|
    I need some ideas. thank you
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  2. #2
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    Quote Originally Posted by ely_en View Post
    Find the minimum value of expression:
    |\cos a|+|\cos b|+|\cos c|+|\cos(a-b)|+|\cos(b-c)|+|\cos(c-a)|
    I need some ideas. thank you
    The smallest value I can find is 2, attained for example when (a,b,c) = (-\pi/2,0,\pi/2). This looks like a local minimum, but I don't see how to prove that it is a global minimum.
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