But this requires that the limit subtraction of the two formulas you separate is meaningful.
Not here.
Secondly, it is wrong to look at your equivalent infinitesimal.
tanx~x
sinx~x
Note that the denominator is (sinx) 3 ~ x 3.
because
The limit of tanx/(sinx) 3 ~ x/x 3 = 1/x 2 is positive infinity.
The limit of sinx/(sinx) 3 ~ x/x 3 = 1/x 2 is positive infinity.
Positive infinity-positive infinity is indefinite.
2. Taylor can also be directly expanded to a certain order (generally not used).
But because the order of denominator is x 3.
Your molecules must swell to at least x 3 to ensure no mistakes.
3. The correct approach:
tanx=sinx/cosx
Primitive up-down multiplication cosx
= (sinx-sinx cosx)/[(sinx) 3 Coase]
Divided by sinx (because the limit, x≠0, just tends to 0)
= (1-cosx)/[(sinx) 2 Coase]
At this time, use equivalent infinitesimal again.
1-cosx~x^2/2
sinx~x
cosx~ 1
=(x^2/2)/[x^2* 1]
= 1/2
So simplify it as much as possible first, and then the equivalent is infinitesimal. Note that only multiplication and division can use equivalent infinitesimal.