化简: $\sin ^{2} \alpha+\sin ^{2} \beta-\sin ^{2} \alpha \sin ^{2} \beta+\cos ^{2} \alpha \cos ^{2} \beta=$
$\sin ^{2} \alpha+\sin ^{2} \beta\left(1-\sin ^{2} \alpha\right)+\cos ^{2} \alpha \cos ^{2} \beta=\sin ^{2} \alpha+\sin ^{2} b \cos ^{2} \alpha+\cos ^{2} \alpha \cos ^{2} \beta=\sin ^{2} \alpha+\cos ^{2} \alpha\left(\sin ^{2} b+\cos ^{2} \beta\right)=\sin ^{2}$ $\alpha+\cos ^{2} \alpha=1$.