AHSME 1973 Problem 17

If $\theta$ is an acute angle and $\sin \frac12 \theta = \sqrt{\frac{x-1}{2x}}$, then $\tan \theta$ equals $\textbf{(A)}\ x \textbf{(B)}\ \frac1{x} \textbf{(C)}\ \frac{\sqrt{x-1}}{x+1} \textbf{(D)}\ \frac{\sqrt{x^2-1}}{x} \textbf{(E)}\ \sqrt{x^2-1}$