(The subject may not have read this paragraph, but I can't help saying that it can be written by mclaughlin formula: sinx = the cubic of x-x+o (the cubic of x), tanx = the cubic of x+x+o (the cubic of x), and then the above sinx-tanx becomes the cubic of negative half x).
The third power of negative one-half x is above, and the third power of one-sixth x is below, which is -3.
Don't worry, now you just need to remember some equivalent infinitesimals, such as the power of a, the equivalence of 1+x 0+AX when x approaches 0, and the rest you can understand by studying Taylor formula.
Pure hand tour, seeking adoption.