11. Given: $\sin \alpha=\cos \beta, \cos \alpha=\sin 2 \beta$, then $\sin ^{2} \beta+\cos ^{2} \alpha=$
11. 0 or $\frac{3}{2} \sin \alpha=\cos \beta(1), \cos \alpha=\sin 2 \beta$ (2) By squaring and adding equations (1) and (2), we get $\sin ^{2} 2 \beta=\sin ^{2} \beta$ Therefore, $\sin ^{2} \beta$ $=0$ or $\cos ^{2} \beta=\frac{1}{4}$, then $\sin ^{2} \beta+\cos ^{2} \alpha=0$ or $\frac{3}{2}$.