when you are determining a formula for cot(2x) using only tan(x) would the formula be...(1-tan^2(x))/(2tan(x))?
yes,
since tan 2x = 2tan x/(1-tan^2 x)
and cot 2x = 1/tan 2x, you formed the reciprocal correctly
since tan 2x = 2tan x/(1-tan^2 x)
and cot 2x = 1/tan 2x, you formed the reciprocal correctly