Simplifying tan²x - csc²x/cot²x and proving a trig identity

[Cabal]

I can, for the mort part, understand how to derive and "proof" most of my Identity work, but some of the more complex (in my feeble opinion) problems give me quite a bit of trouble.

Can anyone explain these?

"Use the fundamental identities to simplify to sines and cosines:
tan(^2)x - (csc(^2)x/cot(^2)x) "
Someone told me the answer was (-1) and I had no idea how to get that.

and

"Confirm the Identity:
(sinx)/(1-cosx) + (sinx)/(1+cosx) = 2cscx"

Any explanations would be greatly appreciated! Thanks!

 

[dextercioby]

HINT:Use the definitions of "composite" functions (tan,cotan,sec,csc) and the fundamental identity
$$\sin^{2}x+\cos^{2}x=1$$

Daniel.

 

[Hurkyl]

My usual advice is to convert everything into sines and cosines, and clear all denominators.