cosa+cosβ=k
sina+sinβ=根号2/2
sina+sinβ+cosa+cosβ=根号2/2+k
根号2sin(a+π/4)+根号2sin(β+π/4)=根号2/2+k
-1<=sin(a+π/4)<=1
-1<=sin(β+π/4)<=1
-2根号2<=根号2/2+k<=2根号2
-5根号2/2<=k<=3根号2/2
-5根号2/2<=cosa+cosβ<=3根号2/2