f(x)=asinxcosx-2cos²x+1=(a/2)sin2x-cos2x.(1)由题设知,0=f(π/8)=(a/2)sin(π/4)-cos(π/4).===>a/2=1.===>a=2.且f(x)=(√2)sin[2x-(π/4)].(2)由题设知,sin[2x-(π/4)]=√2/2.===>2x-(π/4)=π/4.===>x=π/4.