I was thinking about trigonometry ratios, in particularly $\cot(\theta)$, which can be defined as $\cot(\theta) = \frac {1}{\tan(\theta)} = \frac {cos(\theta)}{sin(\theta)}$. Though $\tan(90)$ is not defined as you end up getting $\frac{1}{0}$. Though $\cot(90) = 0$. Though one could interpret that we had to divide it by something undefined as $\frac {1}{0}$, isn't defined. Yet divided by it and we get something defined.
Is it ok to do this?
Is it always ok to divide by something undefined, if it could be flipped in such a way that you get something defined?
Thanks
You may just define $\cot(x) = \frac{\cos(x)}{\sin(x)}$. Then you do not run into problems when evaluating $\cot(\frac\pi2)$.
Without somehow giving a meaning to the term $\frac10$, the equality $\cot(x) = \frac{1}{\tan(x)}$ holds only for those $x$ where $\tan(x)$ is not equal to zero.