2cos2x/sin2x=cotx-tanx
2cos2x/sin2x = 2(cos²x-sin²x)/(2sinx*cosx) = (2cos²x-2sin²x)/(2sinx*cosx) =
= 2cos²x/(2sinx*cosx) - 2sin²x)/(2sinx*cosx) = cos x/ sin x - sinx/cos x =
= cot x-tan x
Left side is equal to right side, so 2cos2x/sin2x=cotx-tanx is true.