Do these two sentence mean the same? must/should in past

I did have to play football. I had to play football. - And here after 'had to' to comes infinitive ?

Are these two sentences the same and are they both correct?


They're both grammatically correct, but they don't mean exactly the same thing.

The normal way of expressing have to in the past is simply had to, as in your second example sentence. For example,

Today I have to go to the office. Yesterday I had to go to the store.

Your first sentence, "I did have to play football", looks like an example of the emphatic do. This is the use of to do as an auxiliary verb to give emphasis to something. For example, if someone said to you, "...but you didn't have to go to the store yesterday," you might respond, "No, I did have to go to the store yesterday." Or you might say, "I didn't have to play football in school, but I did have to play tennis," to emphasize the contrast.

Note that the negation of "have to" in the present or past always uses do, as in

I have to eat


I don't have to eat.


I had to eat


I didn't have to eat.

but in a positive sense, like "I did have to eat", do is not normally necessary.

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