依题意得A=1,则f(x)=sin(x+a), 将M（π/3,1/2）代入得sin(π/3 +a)=1/2,而0＜a＜π,所以π/3＜π/3 +a＜（4π）/3, 所以π/3 +a =(5π）/6 .a=π/2
f(x)=sin(x+π/2)=cosx
f(α)=cosα=3/5,sinα=4/5.f(β)=cosβ=12/13,sinβ=5/13.
f(α-β)=cos(α-β)=cosαcosβ+sinαsinβ=(3/5)*(12/13)+(4/5)*(5/13)=56/65