Verify that each equation is an identity..

Question

tan A= sec a/csca

I have notes (i wasn't here that day and teacher refuses to reteach) but I don't understand them here is the notes...
Problem w/ same directions:
Cos x= cotx/csc x
= Cosx/Sin x / 1/sinx = cosx

I just don't get this?!?!

What don't you understand?
To prove Cos x = cotx/csc x,
Just rewrite it as
(Cosx/Sin x) / (1/sinx) = cosx
It is just algebra.

Similarly,
tan a = sin a/cos a
= (1/csc a)/(1/sec a) = sec a/csc a