Use algebra to prove the identity.

I can't seem to get a 1 on the numerator of the left equation. Here is what I got:

(cosx/1-sin x) - tan x = 1/cos x

(cosx/1-sin x) - sinx/cosx = 1/cos x

(Minus both equations so it looks something like this)

((cosx)(cosx) - sin(1-sin t))/((1-sinx)(cosx))

After the last stage no matter what I do I cannot get just a 1 on the numerator of the left equation. I have tried multiplying out the (cosx)(cosx) to become cos^2x and turning that into -sin^2x + 1 but still I would have a sin left on the top. Please help me with this. Thank you very much!