If = sqrt(3), what is ?

The identity is $1 + \tan^2\theta = \sec^2\theta$.

We are given $\tan\theta = \sqrt{3}$.

Take the square root of both sides:

The given options are A. $\frac{1}{\sqrt{3}}$, B. 1, C. 2, D. $\frac{1}{2}$.
Since 2 is one of the options, and without further information about the quadrant of $\theta$, we select the positive value. If $\tan\theta = \sqrt{3}$, then $\theta$ could be $\frac{\pi}{3}$ (in the first quadrant) where $\sec\theta = 2$, or $\frac{4\pi}{3}$ (in the third quadrant) where $\sec\theta = -2$. Given the multiple-choice options, 2 is the appropriate answer.

The final answer is $\text{C. } 2$.