[tex]\left(1-\dfrac{2\tan x}{\sin 2x}\right)^2=\left(1-\dfrac{2\tan x}{\tan 2x}\right)^2\\\\\left(1-\dfrac{2\cdot\dfrac{\sin x}{\cos x}}{2\sin x\cos x}\right)^2=\left(1-\dfrac{2\tan x}{\dfrac{2\tan x}{1-\tan^2 x}}\right)^2\\\\\left(1-\dfrac{1}{\cos^2 x}\right)^2=\left(1-(1-\tan^2 x)}\right)^2\\\\\left(\dfrac{\cos^2 x-1}{\cos^2 x}\right)^2=\left(\tan^2 x\right)^2\\\\\left(-\dfrac{1-\cos^2 x}{\cos^2 x}\right)^2=\tan^4 x\\\\\left(-\dfrac{\sin^2 x}{\cos^2 x}\right)^2=\tan^4 x[/tex]
[tex]\left(-\tan^2 x\right)^2=\tan^4 x\\\\\tan^4 x=\tan^4 x[/tex]
