Desmos simplifies functions before evaluating them, to save time. Since desmos is a graphing calculator, the small bit of time saved is not insignificant when dealing with the thousands of points required to represent a curve. While Desmos does check for domain errors in basic cases, many times it does not, and you are observing one of them. Desmos evaluates $\frac{1}{NaN}$ to be 0, so for example, try $\frac{1}{\tan(\frac{\pi}{2})}$ and you will get zero as well. Desmos does not however, simplify $\frac{NaN}{NaN}$ or $\frac{0}{0}$ so $\frac{x}{x}$ is undefined at $x=0$