Q:

Article usage in "a cow" vs "the cow"

I have referred to many grammar books and they say that
"A cow gives us milk" and "The cow gives us milk" mean the same thing. They mean all cows give us milk or cows give us milk.
I know that the article "the" talks about the whole class.
Does the indefinite article "a" also talk about the whole class of animals in the given sentence?
I would like to know when a cow and the cow differ in meaning.

A:

We need more context to understand the sentences.  While "The cow" can mean "cows in general", but "Cows" is also used in this sense and might be more common. "The cow" can also mean "that cow, the one we were talking about".  "A cow" means "one cow". 

I have five chickens and a cow. The cow gives us milk.  ("That cow that I just mentioned")
Kind and docile, the cow gives the human race milk.  (Generic use of "the cow", but "cows give the human race milk" would be more common)
You should drink more milk.  A cow would give you that. ("One cow", but it implies that any one cow would do, because all cows give milk)

