Can be expressed equivalently as,
If we "cancel" to get,
Then the functions, will agree on some open interval containing except possiblly at itself.
Thus, the limit exististence and value is equivalent to,
We note that,
by the limit composition rule and one of the famous limits.
Thus, since the functional limits exists so does its sum which is,
Taylor works fast here too, sin(a) =~ tan(a) =~ a for a arround 0, so: