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'Could' is a modal verb used as a more polite way of making a request or asking for permission, to express uncertain possibility, to make a suggestion or offer.
'Could' is a past-tense version of can, indicating what someone or something was able to do in the past.
"Auxiliary-cum-verbs" are :
These 11 auxiliaries are also used as verbs, therefore, they are called Auxiliary–cum–verbs.
These are used to form Tenses. ( Please refer Tense Table).
"Pure Auxiliary verbs" are :
These 20 auxiliaries only support normal verbs, therefore, they are called Pure Auxiliary Verbs. They are also called Models or Model Auxiliary Verbs.