What is the solution to this trigonometric limit problem?

[chmate]

Homework Statement

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

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

 

[Pi-Bond]

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

 

[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.