f(x)=sin(x)+acos(x)+5/8(a)-3/2=1-cosx+acosx+5a/8-3/2=-(cosx-a/2)+a/4+5a/8-1/2∵x∈[0,π/2]∴0<cosx<1当a/2<0,即:a<0时,f(x)的最大值为5a/8-1/2∴5a/8-1/2=1,解得:a=12/5,不合题意,当0<a/2<1,即:0<a<2时,f(x)的最大值为a/4+5a/8-1/2∴a/4+5a/8-1/2=1,解得:a=3/2或a=-4(舍去),当a/2>1,即a>2时,f(x)的最大值为13a/8-1/2∴13a/8-1/2=1,解得:a=12/13,不合题意∴a的值为3/2.