由asinβ+cosβ=1,得a=(1-cosβ)/sinβ
由bsinβ-cosβ=1,得b=(1+cosβ)/sinβ
∴ab=(1-cosβ)(1+cosβ)/(sinβ*sinβ)=(1-(cosβ)^2)/(sinβ)^2=(sinβ)^2/(sinβ)^2=1