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.
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