The correct option is
D cook
The verbs that do not explain the tense of the sentence and do not agree with the subject are called non-finite verbs. Non-finite verbs are usually infinitives, gerunds and participles.NOTE: 'Must' is an auxiliary verb that explains that the sentence is in simple present tense.
Option A - 'I must cooking...' is grammatically incorrect. After 'must' we use the verb in its original form only, because 'must' explains to us that the sentence is in the present tense. Hence, option A is incorrect.
Option B - 'To be cooking' is used in a passive voice only. As the given sentence is in the active voice, we can't use 'to be cooking' here. Hence, option B is incorrect.
Option C - 'To cook' can't be used here, as we use the marker 'to' with the verb to express 'why' some action should be done (For example: I am going to meet him- Why is the action of 'going' done? - To meet him). As the sentence doesn't explain any reason, we can't use 'to cook' here. Hence, option C is incorrect.
Option D - 'Cook' can be used with 'can't' as it doesn't explain the tense of the sentence and also it doesn't relate to the subject. Hence, option D is the correct answer.
'I must cook everyday to become a professional chef.'