Proving cos(nπ+θ)=(-1)^n cos θ and ln|sec x|=-ln|cos x|

[physicsgeek54]

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.

 

[The1337gamer]

For the second one, think about the laws of logarithms you know.

 

[The1337gamer]

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.

 

[Joffan]

For the first one, start by thinking about how $cos(\pi+\theta)$ is related to $cos(\theta)$ - the case where $n=1$

http://www.cliffsnotes.com/study_guide/Addition-Identities.topicArticleId-11658,articleId-11610.html

 

[SammyS]

Use the angle addition identity for the cosine:

cos(A+B)=cos(A)cos(B)-sin(A)sin(B)​