解:f(x)=sin²(x)+2a*cos(x)+3=1-(cosx)^2+2acosx+3=-(cosx)^2+2acos+4=-(cosx)^2+2acos-a^2+4+a^2=-(cosx-a)^2+4+a^2x∈[-π/2,π/6],cosx属于[0,1]①当a=0时f(x)=-(cosx-a)^2+4+a^2=-(cosx)^2+4最大值当cosx=0...