1
a·b=(sinα-1,1)·(1,1-cosα)=sinα-1+1-cosα
=sinα-cosα=1/5
即：1-sin(2α)=1/25
即：sin(2α)=24/25
cosα^2+(1/5+cosα)^2=1
即：25cosα^2+5cosα-12=0
故：cosα=3/5或-4/5
α∈(0,π/2),故：cosα=3/5
sinα=4/5
2
f(x)=5cos(2x-α)+cos2x
=5cos(2x)cosα+5sin(2x)sinα+cos(2x)
=4cos(2x)+4sin(2x)
=4√2sin(2x+π/4)
最小正周期：T=π
对称中心：2x+π/4=kπ
即：x=kπ/2-π/8,k∈Z
故对称中心：(kπ/2-π/8,0),k∈Z
3
x∈[-11π/24,-5π/24]
即：2x+π/4∈[-2π/3,-π/6]
故：sin(2x+π/4)∈[-1,-1/2]
故：f(x)∈[-4√2,-2√2]