Our basis for this equality is the pythagorean theorems of trigonometry. There are three equations for the pythagorean theorems. These are:
sin²x + cos²x =1 1 + tan²x = sec² x 1 + cot² x = csc² x
These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with
cot²x - csc²x = -1
This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.
