lim 1/sin^2(x)--cos^2(x)/x^2
=lim [x^2-1/4sin^2(2x)]/[x^2 sin^2(x)]
=lim [x^2-1/4sin^2(2x)]/x^4 sinx~x(等价无穷小)
=lim[2x-sin2xcos2x]/(4x^3) 罗比达法则
=lim[2x-1/2sin4x]/(4x^3)
=lim[2-2cos4x]/(12x^2) 罗比达法则
=lim[1-cos4x]/(6x^2)
=lim[1/2(16x^2)]/(6x^2) 1-cos4x~(4x)^2/2
=1/2 * 16 / 6
=4/3