高数问题求解‼lim(tanx-sinx)／(sinx)^3 .x趋向0

lim(x→0) (tanx - sinx)/(sinx)^3
= lim(x→0) (tanx - sinx)/x^3,分母等价无穷小
= lim(x→0) sinx(1/cosx - 1)/x^3
= lim(x→0) (sinx)/x * (1 - cosx)/(x^2 * cosx)
= lim(x→0) 2[sin(x/2)]^2/x^2
= lim(x→0) [sin(x/2)]^2/(x/2)^2 * 1/2
= 1/2