Trigo

[icystrike]

1. The problem statement, all variables and given/known data

Show that cos^{2}(\theta)+cos^{4}(\theta)+cos^{6}(\theta)+co s^{8}(\theta)\approx 4cos^{4.3128}(\theta) , \mid\theta\mid\leq\pi/2

and

cos^{2}(\theta)+cos^{4}+...+cos^{30}(\theta)\appro x 15cos^{11.38211}(\theta) , \mid\theta\mid\leq\pi/2

2. Relevant equations



3. The attempt at a solution

Any method?

[LCKurtz]

Well, I don't see how to prove it. Can you give us the context where this problem came from? Where did you find it?

[Berko]

1/(1-x) = 1+x+x^2+...

Isn't there a similar formula if the series terminates?

[icystrike]

LCKurtz: I've actually came up with this question myself cos i saw this relationship for any sum of even power cosine while doing a problem ...

Berko: What do u exactly mean? Please enlighten me :)

[LCKurtz]

1/(1-x) = 1+x+x^2+...

Isn't there a similar formula if the series terminates?

Sure, the problem is a geometric series. And

\sum_{k=1}^4 \cos^{2k}(\theta) = \frac{\cos^2(\theta)-\cos^{10}(\theta)}{1-\cos^2(\theta)}

How does that help?

[icystrike]

Yes! I do recognise that this is a geometric series but nevertheless this cannot lead us to further simplification...:grumpy:

[Berko]

hmm yah I simplified somewhat but not sure where those exponents come from.