How did this transition occur?

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The discussion centers on the limit expression lim as x-> 0 (2-cos3x-cos4x)/(x) and the confusion regarding its transformation into the form (1-cos3x)(1-cos4x)/(x). Participants clarify that the original expression does not equal the factored form mentioned. Instead, it can be rewritten as (1-cos3x) + (1-cos4x). The key point is understanding that the numerator simplifies differently than initially assumed, highlighting the importance of recognizing trigonometric identities in limit calculations.
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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?
 
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kLPantera said:
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?
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)) .
 
So how did the numerator become: (2-cos(3x)-cos(4x)) = (1-cos(3x)) + (1-cos(4x))?
 

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