2. If $3 \sin ^{2} \alpha+2 \sin ^{2} \beta-2 \sin \alpha=0$, then the range of $\cos ^{2} \alpha+\cos ^{2} \beta$ is
A. $\left[\frac{3}{2}, \frac{7}{2}\right]$
B. $\left[\frac{3}{2}, 2\right]$
C. $\left[\frac{14}{9}, 2\right]$
D. $[0,2]$
2. C $2 \sin ^{2} \beta=2 \sin \alpha-3 \sin ^{2} \alpha \in[0,2]$, thus $\sin \alpha \in\left[0, \frac{2}{3}\right]$, and $\cos ^{2} \alpha+\cos ^{2} \beta=2-\sin ^{2} \alpha-\sin ^{2} \beta=$ $2-\sin ^{2} \alpha-\sin \alpha+\frac{3}{2} \sin ^{2} \alpha=\frac{1}{2} \sin ^{2} \alpha-\sin \alpha+2=\frac{1}{2}(\sin \alpha-1)^{2}+\frac{3}{2} \in\left[\frac{14}{9}, 2\right]$.