1.b^2=1,c^2=1,b·c=-cosβ
(b+c)^2=b^2+c^2-2b·c=2-cosβ,∵ 1≤2-cosβ≤3,
∴ (b+c)^2≤3,|b+c|≤√3,即向量b+c长度的最大值为√3.
2.a⊥(b+c),a·(b+c)=0,(cosα,sinα)·(cosβ-1,sinβ)=0,
cos(α-β)=cosα,α=π/4,cos(π/4-β)=cos(π/4),
∴ (π/4)-β=π/4或(π/4)-β=-π/4,β=0或β=π/2,
∴ cosβ=1或cosβ=0.