Answer: a. Prospecting cover letter
Step-by-step explanation:
A prospecting cover letter as the term implies, is one written to inquire about the prospects of working in an organization by way of asking if any jobs are open or to be anticipated in future.
Apart from asking for job openings, one also introduces their selves and shows what qualifications or motivations they might have for wanting to join the organization. All these were done in this excerpt from a letter to Mr. Halverson and so it is most likely a Prospecting cover letter.