AMC 12A 2007 Problem 17

Suppose that \sin a+\sin b=\sqrt{5 / 3} and \cos a+\cos b=1. What is \cos (a-b) ?

Answer Choices
A. \sqrt{\dfrac{5}{3}}-1
B. \dfrac{1}{3}
C. \dfrac{1}{2}
D. \dfrac{2}{3}
E. 1