How do I simplify this?

cos4xcos3x-sin4xcos3x

I pulled the cos3x out as a common factor but that doesn't really help. Can someone please direct me on this. Thanks!

Are you sure is isn't

cos4x*cos3x - sin4x*sin3x ?

That would be cos 7x.

If not, then

cos4x*cos3x - sin4x*cos3x
= cos 3x (cos 4x - sin 4x)
= cos 3x [8 cos^2x -8cos^2 x +1 - 8 cos^3 x sinx + 4 cos x sin x)]

That is not a simplification.

There may have been a typo error in your problem assignment.

Thanks a lot. I also thought the question was written improperly but I spent a lot of time trying to simplify the darn thing! Thanks for your help.

To simplify the expression cos4xcos3x - sin4xcos3x, you correctly identified that cos3x is a common factor. However, you can't simply pull it out and stop there, because you still have two terms that need to be simplified.

Here's how you can proceed:

1. First, factor out cos3x from both terms:
cos3x(cos4x - sin4x)

2. Now, you have cos3x times the expression (cos4x - sin4x). To simplify this further, you need to apply some trigonometric identities.

3. Recall the trigonometric identity: cos(A - B) = cos(A)cos(B) + sin(A)sin(B). You can use this identity to rewrite (cos4x - sin4x) as a single cosine term.

4. Replace (cos4x - sin4x) with cos(4x - 90°), where A = 4x and B = 90°.

Therefore, the simplified expression becomes:
cos3x * cos(4x - 90°)

Now, you have simplified the original expression as much as possible.