Help w/ Math Proofs: cos(n∏+θ), ln|sec x|=-ln|cos x|

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Homework Help Overview

The discussion revolves around two mathematical proofs involving trigonometric identities and logarithmic properties: proving that cos(n∏+θ)=(-1)^n cos θ and ln|sec x|=-ln|cos x|.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring how to approach the proofs, with some suggesting the use of logarithmic laws and others questioning the need for logarithms in the first proof. There is also discussion about expanding the left-hand side of the first equation and considering relevant identities.

Discussion Status

The discussion is active, with participants offering various insights and approaches. Some have suggested specific identities and methods to consider, while others are clarifying assumptions and interpretations of the equations.

Contextual Notes

Participants are navigating the complexities of trigonometric identities and logarithmic properties, with some uncertainty about the necessity of logarithmic concepts in the first proof.

physicsgeek54
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I'm having trouble with these two proofs.
cos(n∏+θ)=(-1)^n cos θ
ln|sec x|= -ln|cos x|

I know for the first one that I have to incorporate log somehow but that's about all I got from it.
 
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For the second one, think about the laws of logarithms you know.
 
For the first one i assume the righthandside means ((-1)^n)cos(theta), how can you expand the left hand side, do you know of any identites or formulae?

I'm pretty sure you don't need log for the first one.
 
For the first one, start by thinking about how [itex]cos(\pi+\theta)[/itex] is related to [itex]cos(\theta)[/itex] - the case where [itex]n=1[/itex]

http://www.cliffsnotes.com/study_guide/Addition-Identities.topicArticleId-11658,articleId-11610.html
 
Last edited by a moderator:
Use the angle addition identity for the cosine:
cos(A+B)=cos(A)cos(B)-sin(A)sin(B)​
 

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