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]

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

 

[Couperin]

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