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Trigonometric limit problem

  1. Sep 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Find [itex]\lim_{x \to 0}\frac{1-cosxcos2xcos3x}{1-cosx}[/itex]

    3. The attempt at a solution

    Actually my book gives this continuation [itex]\lim_{x \to 0}\frac{1-cosx+cosx[1-cos2x+cos2x(1-cos3x)]}{1-cosx}[/itex] but I don't know how author arrived there. Can anyone explain it to me?

    Thank you
     
    Last edited: Sep 4, 2011
  2. jcsd
  3. Sep 4, 2011 #2
    The author rewrote the numerator; if you expand all brackets, you arrive at the same expression.
     
  4. Sep 4, 2011 #3
    Yeah, I realized, after I posted this thread, that author added and substracted [itex]cosx[/itex] in numerator. This was the trick.

    The problem is solved.
     
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