C'mon, you can't be giving yourself a name like that,
What is cosec(x)? it's 1/(Sinx), so cosec(x)/(Sinx) = 1/(Sinx) times 1/(Sinx).
This is written 1/(Sin[sup:27uwv76q]2[/sup:27uwv76q]x), which distinguishes it from 1/(Sin{x[sup:27uwv76q]2[/sup:27uwv76q]}).
Similarly, the other part is 1/(tan[sup:27uwv76q]2[/sup:27uwv76q]x).
Since tanx = Sinx/(Cosx),
1/(tanx) = Cosx/(Sinx), then we have 1/(Sin[sup:27uwv76q]2[/sup:27uwv76q]x) - Cos[sup:27uwv76q]2[/sup:27uwv76q]x/(Sin[sup:27uwv76q]2[/sup:27uwv76q]x).
This is (1-Cos[sup:27uwv76q]2[/sup:27uwv76q]x)/(Sin[sup:27uwv76q]2[/sup:27uwv76q]x) which is Sin[sup:27uwv76q]2[/sup:27uwv76q]x/(Sin[sup:27uwv76q]2[/sup:27uwv76q]x).
Practice with that and try to prove the second one.