Today I had a test for trig and there were two problems that I couldn't get for the life of me. I kept trying over and over and couldn't get them. Can you tell me what I did wrong?

The first one was prove: csc x + cot x = sin x/(1-cos x)

What I did first was make the csc x on the left = 1/sin x. Then I made the cot x= cos x/sin x. I added those together, getting (1+cos x)/sin x.I could not figure out what to do after that.

The next problem I had trouble with was this:

**Simplify down into ONE term**

csc(pi/2-x)(Cos x) - tan(pi-x)- tan x+ cos^2x/(1-(sin^2 x(pi/2 - x))

What I did first was I changed csc(pi/2-x) to sec x. Since sec x = 1/cos x, I multiplied the cos x by it getting 1. Then next I went to the last term and changed the denominator. Since it's 1-sin^2 x(pi/2-x), the sin^2x = cos^2 x.

So that makes the denominator 1-cos^2 x, which equals sin^2 x.

So I end up with 1- tan(pi-x)- tan x+tan^2 x. I was wondering if tan(pi-x) equals cot x like the tan(pi/2- x) identity, does it? Next I added the 1 and the Tan^2 x getting Cot^2 x. So I have Cot^2 x -tan(pi-x)- tan x. Thats where I was stuck and couldn't figure out what to do. Help? Thanks a lot