2010 AMC 12B Problem 20

A geometric sequence (a_n) has a_1=\sin x, a_2=\cos x, and a_3= \tan x for some real number x. For what value of n does a_n=1+\cos x?

\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad \textbf{(E)}\ 8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.