lim(tanx-sinx)/(sinx)^3当x趋于0时的结果怎么求?

lim(tanx-sinx)/(sinx)^3当x趋于0时的结果怎么求?

lim[ (1/cosx-1)sinx]/sin^3(x)
=lim[(1-cosx)/cosx]/sin^2(x)
=lim[x^2/2cosx]/sin^2(x)
=1/2
这里用到了x~sinx 1-cosx~x^2/2
亲,请赐个好评吧.