(1-2cos^2(x))/(sin(x)cos(x))=tan(x)cot(x)

Are you sure you wrote it down correctly? The right-hand side of the equation simplifies to 1. However, that's not what the left-hand side comes out to for most values of x. You can't verify something that's not true!

(SINX/cosx)(cosx/sinx)cross multiply 2sin^2x+2cos^2x/cosxsinx=1-2cos^x/sinxcosx to get cancel 2sin^2x/sinx

Aaah, there's the problem! You missed a PLUS SIGN on the right-hand side of the equation. It should be tan(x) + cot(x). In that case, do just what Sydney said above.