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Sum of square cosines

  1. Dec 3, 2009 #1
    I'm looking for a way to change a finite sum of square cosines:


    into a single function of the sum of x:


    Is there a known way to do this, even if with an approximate method (i.e. Taylor series or such)?. It's ok if it just works in a [tex]\pi[/tex] range.
  2. jcsd
  3. Dec 3, 2009 #2
    Can't be done. If [itex]N=2, x_1=0, x_2=\pi[/itex], sum of x is [itex]\pi[/itex] and sum of cosines is 2. IF [itex]N=2, x_1=\pi/2, x_2=\pi/2[/itex], sum of x is still [itex]\pi[/itex], but sum of cosines is 0.
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