f(x)=(xcosx+cosx+sinx+2)/(cosx+2)=(xcosx+sinx)/(cosx+2)+1,令g(x)=f(x)-1,则g(x)=(xcosx+sinx)/(cosx+2),而g(-x)=(-xcosx-sinx)/(cosx+2)=-g(x),∴g(x)是奇函数,g(x)的最大值显然为M-1,最小值为m-1,而最大值与最小值是互为相反数的,所以M-1+m-1=0,M+m=2