Things to check for hyper trigonometry

[Phryxia]

Equivalence Test

Hyper trigonometric functions are actually can be expressed without them.

Consider the sinh function which has popular three equivalent forms.

Determining the equivalence of hyper trigonometric functions is exactly same problem to that of primary operation (+, -, *, / and ^) By assuming primary operation equivalence determination works ideally, all we have to do is just compare the equivalence of basic form. (For sinh, it can be one of the expressions in above image)