How is this trig identity equal? I do not understand how this is equal.
$$
{cos\theta(cos\theta-1)\over 1-cos\theta} = -cos\theta
$$
What simplification step am I missing? Thanks.

$${\cos\theta(\cos\theta-1)\over 1-\cos\theta} = -\cos\theta $$
$$\iff \cos\theta(\cos\theta-1)=-\cos\theta(1-\cos\theta)$$
$$\iff \cos^2\theta - \cos\theta = \cos^2\theta - \cos\theta $$
