AMC 12B 2010 Problem 13

[system]

In \triangle A B C, \cos (2 A-B)+\sin (A+B)=2 and A B=4. What is B C ?

Answer Choices
A. \sqrt{2}
B. \sqrt{3}
C. 2
D. 2 \sqrt{2}
E. 2 \sqrt{3}