x趋于0 lim sinx-tanx/x^3=lim sinx/x×(cosx-1)/(x^2×cosx)是怎么通分的?

题目

x趋于0 lim sinx-tanx/x^3=lim sinx/x×(cosx-1)/(x^2×cosx)是怎么通分的?
x趋于0 lim sinx-tanx/x^3=lim sinx/x×(cosx-1)/(x^2×cosx)
thank you

答案

(sinx-tanx)/x^3
=sinx (1- 1/cosx)/x^3
=[sinx(cosx-1)]/cosx x^3
分子分母同时除以x
sinx/x×(cosx-1)/(x^2×cosx)