6. Given $\cos x+\cos y=\frac{1}{2}, \sin x+\sin y=\frac{1}{3},$ the value of $\cos (x-y)$ is ( ).
A. $-\frac{59}{72}$
B. $-\sqrt{\frac{59}{72}}$
C. $\frac{59}{72}$
D. $\sqrt{\frac{59}{72}}$
6. A. $(\cos x+\cos y)^{2}+(\sin x+\sin y)^{2}=2+2 \cos (x-y)=\frac{1}{4}+\frac{1}{9}$, so $\cos (x-y)=-\frac{59}{72}$.