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Show this simple trigonometric identity add up to 0

  • Thread starter td21
  • Start date
  • #1
td21
Gold Member
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8

Homework Statement


[tex]\cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L})[/tex]


Homework Equations





The Attempt at a Solution


the first cosine is the same as positive but is the second cosine simply equal to
[tex]\cos (\frac{\pi x}{L})[/tex]?


thanks!
 

Answers and Replies

  • #2
verty
Homework Helper
2,164
198
When x = 1, L = 3, we have:

cos(-pi/3) - cos(pi)
= 1 + cos(-pi/3) > 0
 
  • #3
Mentallic
Homework Helper
3,798
94
[tex]\cos(-x)=\cos(x)[/tex]
and
[tex]\cos(3x)=4\cos^3(x)-3\cos(x)[/tex]

So obviously this isn't going to be equal to 0 for all x.
 

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