Simplifying a cosine + cosine with conjugate denominators

[luckyduck]

Homework Statement

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

Homework Equations

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

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?

Thanks in advance for all your help!

 

[Mark44]

Homework Statement

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

Homework Equations

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

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?

Thanks in advance for all your help!

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

 

[luckyduck]

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

 

[Mark44]

What are you getting?

 

[LCKurtz]

Homework Statement

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

What are you getting?

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