I need assistance in what identities I am able to utilize in order to resolve or simplify the double angle identity. I have tried converting the cos2x in all its three forms in order to simplify, however, nothing seems to function.

Use
the cosine of double argument formula cos 2x = cos^{2}x
– sin^{2}x
and factor it by using the difference of squares formula cos 2x =
cos^{2}x
– sin^{2}x
= (cos x – sinx)(cos x + sinx).

Then
– cos2x / (sin x – cos x)^{2}
= (sin x – cosx)(sin x + cosx) / (sin x – cos
x)^{2}
=

(sin
x + cosx)
/ (sin x – cos x).

If necessary, continue by dividing both the numerator and denominator by cos x

(tan x + 1) / (tan x - 1) = note that tan(π/4)
= 1

- (tan x + tan(π/4)) / (1 - tan x * tan(π/4) ) = use the tangent of the sum formula