f(x)=(1+cos2x+8(sinx)^2)/sin2x =(2(cosx)^2+8(sinx)^2)/2sinxcosx =cosx/sinx+ 4sinx/cosx >=4当且仅当cosx=2sinx,即x=artcot2时取等号。所以 f(x)的最小值是4