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