Simplifying a cosine + cosine with conjugate denominators

1. Mar 13, 2013

luckyduck

1. The problem statement, all variables and given/known data

-$\frac{1}{2}$[cos($\frac{\pi+\pi n}{\pi+\pi n}$) + cos($\frac{\pi-\pi n}{\pi-\pi n}$)]

2. Relevant equations

cos(u)cos(v) = $\frac{1}{2}$ cos(u+v)+cos(u-v)

3. The attempt at a solution
I am attempting to use the above trig function to simplify the first function, but I can't seem to do it properly. Is there another function for when the contents of the cos are equal to its denominator?

2. Mar 13, 2013

Staff: Mentor

Don't the fractions simplify to 1 for nearly all values of n? BTW, are there any restrictions on n?

3. Mar 13, 2013

luckyduck

I keep getting weird numbers. Problem doesn't state any restrictions!

4. Mar 13, 2013

Staff: Mentor

What are you getting?

5. Mar 13, 2013

LCKurtz

More to the point, where did that expression come from? I'm guessing almost certainly from an incorrectly worked Fourier Series problem.