I'm looking for a hint on how to prove that
I know I'm on here a lot but I really have no one to go to for guidance and am trying to learn this material on my own from the text book. Thank you for being patient with me so far and for being so helpful.
Thanks guys. I was able to do it via induction but I think it was intended that I use some more direct method. It says "obtain the formula" I tried complexification as mr. fantastic recommended and obtained some interesting results but nothing I could use trig identities to simplify into the required form.
Also I was wondering if there is a closed form of or . I figured if there is such a formula it might come in handy here.
I've also tried using the infinite series definition of cosine and sine and again came up with interesting results but nothing that would help me unless I had a formula for the series I just mentioned.
Thank you two for your help thus far. I really just wish my book had more examples that I could build on for these problems. Does anyone know of some catalogue of proofs that I could look at to get some more inspiration?
You're missing the i's (I was tempted to say you have no i-dea, open your i's etc. ....)
Anyway, it's meant to be . Do you see the i? It is important (each word starts with i ....)
Now use the formula for the sum of a geometric series where the first term is , and there are n terms in the series. Then get the real part of the result. Refer to my previous post.
Darn it! I always make mistakes like those. Thank you for that
so *I* have
Is this right so far? Because what comes after when I apply Euler's identity again is a god forsaken mess when I try to get the real part.
Just to show I'm doing the work though
Then comes the process of making the denominator real by multiplying by a conjugate over a conjugate. I'd show you the work I've done for that but unfortunately the size limit for the LaTeX images created prohibits me from doing so.
How does this reduce?
Ahhh
So what we really have is
Which then leaves an left in that term when we bring down the so we have
Using Euler again
Taking the real part of which leaves me
Wow it's finally done. Thank you so so very much for your help. Thank goodness it's finally done!