Hey all, so I had a question where it seems that points of discontinuity are just disappearing. Take a look:

$\displaystyle cot(\theta)=\frac{1}{tan(\theta)}=\frac{1}{\frac{s in(\theta)}{cos(\theta)}}$$\displaystyle =\frac{cos(\theta)}{sin(\theta)}$

So, when I have the $\displaystyle \frac{1}{tan(\theta)}$, the points of discontinuity are wherever $\displaystyle tan(\theta)$ is 0 or discontinuous, which occurs whenever $\displaystyle sin(\theta)=0$ or $\displaystyle cos(\theta)=0$, but when I have $\displaystyle \frac{cos(\theta)}{sin(\theta)}$, the only points of discontinuity are when $\displaystyle sin(\theta)=0$. Am I crazy or did a point of discontinuity just disappear through a simple rearrangement? What is going on here?