To simplify the given expression, we need to use the trigonometric identity:
1 - tan^2(x) = sec^2(x)

Therefore, we can rewrite the expression as:
2tg(2x)/sec^2(2x) = sqrt(3)

Using the definition of tangent and secant functions:
2sin(2x)/cos(2x) = sqrt(3)

Now, let's simplify the expression further:
2sin(2x) = sqrt(3)cos(2x)

Next, we can divide both sides by cos(2x):
2tan(2x) = sqrt(3)

Therefore, the simplified expression is:
2tan(2x) = sqrt(3)