How to find the limit x approaches 0 of (sin x-tan x)/x^3

lim(x→0) (sin x - tan x)/x^3
= lim(x→0) sin x (1 - 1/cos x)/x^3
= lim(x→0) (sin x/x) * (cos x - 1)/(x^2 cos x)
= 1 * lim(x→0) (-1/cos x) * (1 - cos x)/x^2
= 1 * (-1/1) * lim(x→0) (1 - cos x)/x^2
= -1 * lim(x→0) (1 - cos x)/x^2
= -1 * lim(x→0) (1 - cos x)(1 + cos x)/ [x^2 (1 + cos x)]
= -1 * lim(x→0) (1 - cos^2(x)) / [x^2 (1 + cos x)]
= -1 * lim(x→0) sin^2(x) / [x^2 (1 + cos x)]
= -1 * lim(x→0) (sin x/x)^2 * [1 / (1 + cos x)]
= -1 * 1^2 * (1/2)
= -1/2.

I hope this helps!