Stuck On Some Trig Identities

I was having trouble with a few problems none of my friends could help me with, so I figured I'd give this forum a try. Thanks in advance, here are the problems:

Establishing the Identities of (1-sin^2x)/(1-cosx)=-cosx (I'm not sure how to make thetas) and (1-cotx^2)/(1+cotx^2)=1-2cosx

cos x = 3/5, 0 < x < 2pi, What is cos(2x)?

And lastly, find the exact value of these two:

cos(2tan^-1(4/3))

sec(tan^-1(4/3)+cot^-1(5/12))

Hopefully that wasn't too hard to read, any help on any problem would be VERY appreciated, thanks a lot!