# How did this transition occur?

1. Oct 5, 2012

### kLPantera

lim as x-> 0 (2-cos3x-cos4x)/(x).

I'm not sure how the numerator became (1-cos3x)(1-cos4x)/(x)

What am I missing? Could someone please point it out? Is it a trignometric factoring formula I'm not thinking of?

2. Oct 5, 2012

### SammyS

Staff Emeritus
It's difficult to answer this without you providing more context, but here's a try.

(2-cos(3x)-cos(4x)) ≠ (1-cos(3x))(1-cos(4x)).

However, (2-cos(3x)-cos(4x)) = (1-cos(3x)) + (1-cos(4x)) .

3. Oct 5, 2012

### kLPantera

So how did the numerator become: (2-cos(3x)-cos(4x)) = (1-cos(3x)) + (1-cos(4x))?