f(x)= (1+cos2x+8sin^2x)/sin2x = (2cos^2x+8sin^2x)/2sinxcosx = (cos^2x+4sin^2x)/sinxcosx = cotx+4tanx 然后用均值不等式可得出结论.-_-0=2(1/a*4a)^(1/2)=4当且仅当1/a=4aa=1/2时等号成立...