f(x)=cos2x-5cosx+3=2cos²x-1-5cosx+3=2cos²x-5cosx+2=2(cosx-5/4)²-9/8∵cosx∈[-1,1],∴f(x)max=2(-1-5/4)²-9/8=9,f(x)min=2(1-5/4)²-9/8=-1