As we all know, math is a minimalistic science. For example we don't put into the definition of differentiable functions that they have to be continuous. So my question is this:
What's the idea of defining such a thing like cosecant or secant? I have never seen their use in math or other science.
If you're asking how they are defined then: $$\sec(x) = \frac{1}{\cos(x)}$$ and $$\csc(x) = \frac{1}{\sin(x)}$$
If you're asking when the are used, almost everything in higher level math or physics relies on some knowledge of trigonometry. For example, when you take a Complex Analysis Class, knowledge of trigonometric functions is heavily used.