AMC 12B 2010 Problem 20

A geometric sequence \left(a_{n}\right) 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 ?

Answer Choices
A. 4
B. 5
C. 6
D. 7
E. 8