sec(arctan(2x))

We are looking for the secant of an angle whose tangent = 2x  = 2x / 1

So, r = √(4x^2 + 1)

So, the secant = r / x =  ± √(4x^2 + 1) .....remember, that "x" could be positive or negative 1 since the tangent is positive.....