A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
maheshmeghwal9
 2 years ago
Prove that if \[x+\frac{1}{x}=2 \cos \alpha,\] then
\[x^n+\frac{1}{x^n}= 2\cos n \alpha.\].
[This problem is based on DeMoivre's theorem]
maheshmeghwal9
 2 years ago
Prove that if \[x+\frac{1}{x}=2 \cos \alpha,\] then \[x^n+\frac{1}{x^n}= 2\cos n \alpha.\]. [This problem is based on DeMoivre's theorem]

This Question is Closed

maheshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0I have done like this:  Let \[x= e^{i \theta}\]&\[\frac{1}{x}=e^{i \theta}\]This approach is also given in my book. But now how to do further ? This is my actual problem.

maheshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0@ujjwal @zepp @zzr0ck3r Plz help:)

ujjwal
 2 years ago
Best ResponseYou've already chosen the best response.1\[x+\frac{1}{x}=2\cos \alpha\]only when x=1 and \(\alpha\)=0 This relation is not satisfied by any other values.

ujjwal
 2 years ago
Best ResponseYou've already chosen the best response.1So, the second part goes accordingly!

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.2\[r\left(e^{i\theta} + e^{ i \theta}\right) = 2\cos \alpha\]

ujjwal
 2 years ago
Best ResponseYou've already chosen the best response.1Contd. \(x^n\)=1 and n\(\alpha\)=0 for any value of zero Remember we already have x=1 and \(\alpha\)=0

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.2\[x^n = e^{ni\theta}\]

maheshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0I gt that but isn't there logical way @ujjwal ?

ujjwal
 2 years ago
Best ResponseYou've already chosen the best response.1*n In my last reply zero=n..

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.2\[x^n + \frac1{x^n} = e^{ni\theta}+e^{ni\theta} = \cos n \theta + i\sin n\theta +\cos n \theta  i\sin n\theta = 2\cos n \theta \]

ujjwal
 2 years ago
Best ResponseYou've already chosen the best response.1I know that is informal and there must be a very formal way to derive that relation.. And @Ishaan94 is giving it to you.

maheshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0oh ok i see :) thanx to all for the help :)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.