Proving this trigonometric identity

  • Thread starter Couperin
  • Start date
  • #1
57
0

Homework Statement



Prove the following identity: [tex](1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta)[/tex]

Homework Equations



[tex]cos^2 \theta + sin^2 \theta = 1[/tex]

The Attempt at a Solution



I've squared out the first bracket so that it becomes [tex]1 + cos^2 \theta[/tex] and multiplied out the second bracket so that it becomes [tex]2 + 2cos \theta[/tex]. With some rearrangement I get [tex]cos^2 \theta + sin^2 \theta = 1 + 2cos \theta[/tex]

I can't get rid of the 2cos, and I think it's because I'm doing something wrong when squaring out that first bracket. But I can't see what it is that I'm doing wrong, only that [tex]1 + cos^2 \theta[/tex] doesn't = [tex](1 + cos \theta)^2[/tex].

What am I doing wrong?
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
73
[tex](1+\cos\theta)^2=1+2\cos\theta+\cos^2\theta[/itex]
 
  • #3
57
0
Ahh thank you! Looks like I forgot a very simple rule of algebra. I hate it when that happens XD.
 

Related Threads on Proving this trigonometric identity

  • Last Post
Replies
17
Views
4K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
2
Views
2K
Top