f(x)=cosx^4-2sinxcosx-sinx^4
=(cosx^2+sinx^2)(cosx^2-sinx^2)-sin2x
=1*cos2x-sin2x
=cos2x-sin2x
=√2cos(2x+Π/4)
因为cos(2x+Π/4)的值域为[-1,1]
所以f(x)的值域为[-√2,√2]