Use De Moivre's Theorem to prove this:

  • #1
Use De Moivre's Theorem to show that for any n greater that equal to 1

(1+itanθ)n + (1-itanθ)n =2cosnθ/cosnθ

where cosθ ≠ 0


I tried to approach this by converting into modulus argument form but wasn't really sure if that was correct. It's a common New South Wales HSC question but I couldn't find a solution anywhere. Help would be greatly appreciated :)
 

Answers and Replies

  • #2
100
0
The first step would be to convert tanθ into [itex]\frac{sin\theta}{cos\theta}[/itex] and work from there.
 
  • #3
Thanks a bunch - that helped a lot. Converted it into:
[(secθ)(cosθ+isinθ)]^n + [(secθ)(cosθ-isinθ)]^n and it was easy from there.

Cheers!
 
  • #4
100
0
No problem. Good luck with the HSC, I just finished mine :P
 

Related Threads on Use De Moivre's Theorem to prove this:

  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
6
Views
2K
  • Last Post
2
Replies
33
Views
4K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
931
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
6
Views
3K
Top