# 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.