∵f(x)=a[cos^2(x)+sinxcosx]+b=a[(1+cos2x)/2+(1/2)(2sinxcosx)]+b=a[(1/2)sin2x+(1/2)cos2x+1/2]+b=a[(1/2)(sin2x+cos2x)]+(a+2b)/2=(√2a/2)sin(2x+π/4)+(a+2b)/2∵x∈[0,π/2]∴2x+π/4∈[π/4,5π/4]∴sin(2x+...