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Trigonometry problem help

  1. Sep 6, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the solution of
    2(cos x + cos 2x)+sin 2x(1+2cos x)=2 sin x in the interval [-pi, pi]

    3. The attempt at a solution
    2 (cos x- sin x)+ sin 2x +cos 2x +2sin 2x cos x=0
    2 (cos x- sin x)+ sin 2x +cos 2x +sin 3x+sin x=0
    cos 2x+2cos x+sin 2x-sin x+sin 3x=0

    But now its difficult to convert into factors to apply zero prouct rule.
  2. jcsd
  3. Sep 6, 2008 #2


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    Staff Emeritus
    Science Advisor

    Re: Trigonometry

    I would recommend you get rid of "sin 2x" and "cos 2x" by using sin 2x= 2sin x cos x and cos 2x= cos2 x- sin2 x.
  4. Sep 7, 2008 #3
    Re: Trigonometry

    Changing all the multiples of x, I get:
    cos2x+2 cos x +2 sin x cos x -4 sin3x+2sin x -sin 2x=0

    cos x(cos x+sin x +2)+sin x(2cos 2x+sin x)=0

    Again I am stuck?????
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