Final answer:
Tuberculosis is the drug-resistant disease that can be transmitted through coughing, caused by Mycobacterium tuberculosis, and known for its potential to develop drug resistance.
Step-by-step explanation:
The disease that is potentially drug resistant and thought to be transmitted through coughing is tuberculosis. Tuberculosis, caused by Mycobacterium tuberculosis, is known for its ability to develop resistance to drugs. It is a highly infectious disease that is spread primarily through aerosols that are produced when an infected person coughs, sneezes, or spits.
Diphtheria, although transmitted through coughing, does not typically develop drug resistance. It is caused by Corynebacterium diphtheriae. Pertussis, or whooping cough, caused by Bordetella pertussis, is also spread through coughing, but it was not one of the options provided.
Concerning the other part of the question, Q fever is caused by Coxiella burnetii, which is not transmitted by coughing but can be transmitted through inhalation of barnyard dust contaminated by infected animals.