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Hello, I have a really tricky question today, so I need your help. Please help me out.

I know that the past tense of "must" is "had to". Then, how can I distinguish between the past tense of "must" and that of" have to" And what is the past tense of "should" then? Is this also "had to"?

Thank you as usual and have a good day all.
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'Had to' is not the past tense of 'must'; 'must' has no past tense. In some contexts, if we wish to express the idea of an obligation imposed in the past, we can use 'had to'

'Should' has several shades of meaning. In the sense of weak obligation, as in "I should go now", one way of expressing this as a past form is 'was supposed to".
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"Must" is a defective/modal auxiliary and you should learn the various meanings and uses of these verbs separately. "Must" has no past tense; "had" is the past tense of "have".

Very often, a perfect infinitive is used with the modal auxiliaries to refer to the past. Examples:

It must be easy. (now, tomorrow)
It must have been easy. (yesterday)

"Should" is another modal auxilary.

We should do it. (now, tomorrow)
We should have done it.. (yesterday)

Some modals do have a past tense but it may not be possible to always use it.

He can swim very well.
He could swim very well when he was five years old.

CB
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Comments  
Yes, this is tricky. Conditionals are the most complex topic in English. Conditionals are used to indicate uncertainty, tentativeness, probability, etc. Typically they are used in present time with sometimes a seeming implication of future time:

"I may go to the party." (This is said in present time, indicating uncertainty, yet there seems to be an implied futureness about it, as the party is in future time.)

"I might go to the party." ("Might" is nominally the past of "may," and yet this is not past time. This is, again, present, with a sort of implied futureness. "Might" implies slightly more tentativeness than "may.")

Since conditionals indicate uncertainty, their use in the past is rather awkward, since if an event has already happened, then there technically should be no uncertainty about it. For example:

"I must be at the party." (This is present time - with seeming implied futureness.)

How would this be said in past time? Rather awkward, in a way. Maybe:

"I knew I must be at the party."

Similarly:

"I should show up at the party." (Present time, implied futureness.)

Past? Maybe:

"I knew I should show up at the party."
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The best way is to use Should + have + V3 or Ved.

For example: I should have studied.

This is a great video about it:
https://www.engvid.com/grammar-past-tense-should /