14. Given $\sin \alpha+\sin \beta=1$, find the range of $\cos \alpha+\cos \beta$.
14. Let $u=\cos \alpha+\cos \beta$, then $(\sin \alpha+\sin \beta)^{2}+(\cos \alpha+\cos \beta)^{2}=1+u^{2}=2+2 \cos (\alpha-$ $\beta)$, so $u^{2}=1+2 \cos (\alpha-\beta)$. Therefore $0 \leqslant u^{2} \leqslant 3$, then $-\sqrt{3} \leqslant u \leqslant \sqrt{3}$, which means the range of $\cos \alpha+\cos \beta$ is $[-\sqrt{3}, \sqrt{3}]$.