函数f(x)=-1/2-a/4+acosx+(sinx)^2(0≤x≤π/2)的最大值为2,求实数a的值

f(x)=-(cosx)^2+acosx-a/4+1/2=-[(cosx)^2-acosx]-a/4+1/2=-[(cosx)^2-acosx+a^2/4]+a^2/4-a/4+1/2=-(cosx-a/2)^2+a^2/4-a/4+1/2=-(cosx-a/2)^2+1/4[a^2-a]+1/2=-(cosx-a/2)^2+1/4[a^2-a+1/4]-1/16+1/2=-(cosx-a/2)^...