First check that the supposed identity is correct by substituting a value for x. Let x=45°, so tan(x)=1. sec(x)=√2, sec2(x)=2.
LHS is 4tan(x)=4. RHS is 2(2)/(2-4)=4/-2=-2. So LHS≠RHS and the identity as false.
2-2sec2(x)=-2tan2(x), so 2(2tan(x))/(2-2sec2(x))=4tan(x)/(-2tan2(x))=-2cot(x).