2tanx/1-tan^2x = 2/cotx-tanx

2tanx/1-tan^2x = tan2x = sin2x/cos2x

= 2sinx*cosx/ (cos^2x - sin^2x). Divide numerator and denomenator by sinx*cosx, you get

= 2/(cotx - tanx)

csc^2x/cox^2x = sec^2x + csc^2

sec^2x + csc^2

= 1/cos^2x + 1/sin^2x

= (sin^2x + cos^2x)/ sin^2x*cos^2x

= 1/(sin^2x*cos^2x)

= csc^2x/cos^2x