3 Given $\frac{\cos \alpha \cos \frac{\beta}{2}}{\cos \left(\alpha-\frac{\beta}{2}\right)}+\frac{\cos \beta \cos \frac{\alpha}{2}}{\cos \left(\beta-\frac{\alpha}{2}\right)}=1$. Then the value of $\cos \alpha+\cos \beta$ is
A. 1
B. $\frac{1}{2}$
C. $\sqrt{2}$
D. $\frac{\sqrt{2}}{2}$