Simplifying a cosine + cosine with conjugate denominators

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Homework Help Overview

The discussion revolves around simplifying an expression involving cosine functions with conjugate denominators. The problem is situated within the context of trigonometric identities and simplification techniques.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to apply trigonometric identities to simplify the expression but are encountering difficulties. Questions arise regarding the behavior of the fractions when the contents of the cosine functions equal their denominators, and whether there are any restrictions on the variable n.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and experiences with the problem. Some express confusion over the results they are obtaining, while others inquire about the origin of the expression and its potential connection to Fourier Series.

Contextual Notes

There is mention of a lack of stated restrictions on the variable n, which may affect the simplification process. Participants are questioning the assumptions underlying the problem setup.

luckyduck
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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!
 
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luckyduck said:

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?
 
I keep getting weird numbers. Problem doesn't state any restrictions!
 
luckyduck said:

Homework Statement



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

Mark44 said:
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.
 

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