y=(sin^2x+1)(cos^2x+1)/(sin^2xcos^2x)
=(sin^2xcos^2x+2)/(sin^2xcos^2x)
=1+8/(sin2x)^2
容易知道,当(sin2x)^2取最大值时候,y有最小值,最小值=ymin=1+8=9.