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(1) f=A/2﹣A/2*cos(2wx+2φ),最大值是2,则当cos(2wx+2φ)=-1时f最大,故A=2
对称轴间距为2,则周期为4,2π/(2w)=4,得w=π/4
f=1-cos(π/2*x+2φ),代入点(1,2),得sin2φ=π/2+2kπ,由约束条件0＜φ＜π/2,得φ=π/4
(2) f=1-cos(π/2*x+π/2)=1+sin(π/2*x)
f(1)+f(2)+f(3)+f(4)=4
f(5)+f(6)+f(7)+f(8)=4
……
f(2005)+f(2006)+f(2007)+f(2008)=4
故f(1)+f(2)+……+f(2008)=4×502=2008