Question

if i have cos(4*pi*x - n*pi*x) what property or rule allows me to rewrite it as cos(4-n)*pi*x ?

Answer 1

how about factoring the \(\pi x\) ?

Answer 2

um okay. what rule states you can factor something out of a trig function like that?

Answer 3

not the function.. just the angle in the function
\[
\cos\left(4\pi x-n\pi x\right)=\cos\left[(4-n)\pi x\right]
\]

Answer 4

okay how does that angle end up on the otherside like \[\cos(4-n)\pi*x\]

Answer 5

better question, help me integrate : \[\int\limits_{-1}^{0}\cos(4 \pi x)\cos(n \pi x) dx\]

Answer 6

use the addition rule \[\cos C\cdot\cos D={1\over2}\left[\cos(C+D)+\cos(C-D)\right]\]