$\displaystyle sec(tan^{-1} 2x)$
I think the 2x has something to do with why I can't solve this problem, but even then, I still don't remember what to do about it...
Recall $\displaystyle \tan\theta=\dfrac{\text{opp}}{\text{adj}}$. So in the case of $\displaystyle \tan\theta=2x$, 2x is the side opposite of $\displaystyle \theta$, and 1 is the side adjacent to $\displaystyle \theta$.
As a result, the hypotenuse of the triangle is $\displaystyle \sqrt{1+4x^2}$ (verify).
Now what is $\displaystyle \sec\theta$?