# Trigonometric limit problem

1. Sep 4, 2011

### chmate

1. The problem statement, all variables and given/known data

Find $\lim_{x \to 0}\frac{1-cosxcos2xcos3x}{1-cosx}$

3. The attempt at a solution

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

Thank you

Last edited: Sep 4, 2011
2. Sep 4, 2011

### Pi-Bond

The author rewrote the numerator; if you expand all brackets, you arrive at the same expression.

3. Sep 4, 2011

### chmate

Yeah, I realized, after I posted this thread, that author added and substracted $cosx$ in numerator. This was the trick.

The problem is solved.