Proving this trigonometric identity

[Couperin]

Homework Statement

Prove the following identity: $$(1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta)$$

Homework Equations

$$cos^2 \theta + sin^2 \theta = 1$$

The Attempt at a Solution

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

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 $$1 + cos^2 \theta$$ doesn't = $$(1 + cos \theta)^2$$.

What am I doing wrong?

 

[cristo]

[tex](1+\cos\theta)^2=1+2\cos\theta+\cos^2\theta[/itex][/tex]

 

[Couperin]

Ahh thank you! Looks like I forgot a very simple rule of algebra. I hate it when that happens XD.