this is the first time I've asked a question here, so bare with me...
I'm in Year 12 Maths B (kinda like Maths Extension) and, though we have not been told anything at all whatsoever about Cosecant, Secant and Cotangent, I got curious. Please excuse my comparatively limited knowledge of mathematics.
So, I had to differentiate $\frac{1}{\tan(x)}$ into it's simplest form, and I have no source of answers to check with, so I used Wolfram|Alpha. It told me that the simplest form was $\csc^2(x)$ (by the way, sorry if I haven't yet discovered how to make maths look proper on this page) which got me confused. After many research, I discovered that these other three trigonometric functions are the reciprocals of the major three. So, working through my problem, I got to this point:
$$-\sec^2(x) \cot^2(x) = -\csc^2(x)$$
This is where my understanding fails. What processes exist between the two equations immediately above this text? Why does $$-\sec^2(x) \cot^2(x) = -\csc^2(x)$$
A detailed, step-by-step instruction on how/why this is what it is would really help me understand, and would be much appreciated.