I have confusion with some grammatical facts. So I am looking for help here.
Which one should be correct?
A. What did you use to cook?
B. What did you used to cook?
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I voted to close because this has been asked and answered more that once before, but I can't resist flagging up this somewhat striking example...
That's actually from a book intended to teach English to non-native speakers! The writer seems blissfully unaware that he's written the past tense both different ways in the same sentence. I think that's proof enough of my comment that there is no "correct" orthography. (But I'd expect any halfway competent teacher to be at least consistent! :)
Note that there's no possibility of ambiguity (doubt as to whether What did you use(d) to cook? means A: What implements did you use to cook?, or B: What did you usually cook?), because they're enunciated completely differently. The first meaning always has a soft "Z", whereas the second always has a hard "S" sound, and blends seamlessly into the infinitive marker that follows (as usta).
EDIT: (2 days after original post)
I must accept at least one of the points made in the extended discussion my answer led to (now moved to chat). If we rephrase slightly and switch to a different verb...
1: Explain what you wanted to do.
2: Explain what you didn't want to do.
...it should be clear that the second version doesn't inflect want for Past Tense. That's because we've already done this with the auxiliary verb did (so have is just an "unmarked infinitive", that doesn't include the "infinitive marker" to [have] in such contexts).
But my substantive point is that few native speakers would consciously recognise that point for OP's exact example, and most (if not all) of us can neither pronounce nor hear the difference between use and used in such contexts, so it doesn't really make much difference how it's written.
In my speech, I never use "use(d) to" in the primary clauses of questions in this way.
However, many English speakers do (it is dialectual). It's always "used to" with the first person ("I"/"we"). "Use" is more common than "used" with second ("you") person, but I've heard both ("used" is common in the Southern US and in AAVE). Some websites will say it is incorrect that way, but it is definitely in use.
However, there is another problem with the diction here.
What did you use to cook?
^ This sounds like you might be using the phrase 'use to' in a different way - asking what tools or items were used to help you cook! "What did you use to cook? Did you use the spatula? Did you use the knife?" So I would find another way to disambiguate or convey your actual meaning, perhaps:
What dishes did you use to cook?
or avoid "use(d) to" altogether.
If you say it in the southern english / AAVE way ("you... used to") - your B) above - it's not ambiguous, and fine as is.