y=(sinθ+cosθ+1) /( sinθcosθ ) 设t=sinθ+cosθ=√2sin(θ+π/4) t∈[-√2,√2],t≠±1∴t²=1+2sinθcosθ∴sinθcosθ=(t²-1)/2∴y=(t+1)/[(t²-1)/2] =2/(t-1) ∵ t∈[-√2,√2],t≠±1∴ -√2-1≤t-1<-2,-2∴函数的值域为 (-∞,-1)U (-1, 2-2√2)U [2(√2+1),+∞) 最值不存在吧