Simplifying trignometric expression

Question

How does the denominator on the left become the denominator on the right. When I try to simplify it, I get $-2\cos^2(\theta)+2\cos \theta$. What am I doing wrong... please help.

Answer 1

$1-\cos^2 (\theta) = (1+\cos(\theta)) (1-\cos (\theta))$

$1-2\cos(\theta)+\cos^2(\theta) = (1-\cos(\theta))^2$

$\therefore (1-\cos^2 (\theta))-(1-2\cos(\theta)+\cos^2(\theta)) = (1-\cos (\theta))(1+\cos(\theta))-(1-\cos(\theta))^2 = (1-\cos (\theta)) [1+\cos(\theta)-(1-\cos(\theta))] = ((1-\cos(\theta))(2\cos(\theta))$