Final answer:
The client is using denial, an unconscious defense mechanism to protect themselves from the painful truth about their condition related to smoking and lung cancer.
Step-by-step explanation:
The defense mechanism the client is using is denial. Denial is an unconscious refusal to accept reality or facts. It is a way for individuals to protect themselves from painful truths. In this case, the client with lung cancer and a history of smoking is attributing their cough to a common cold rather than acknowledging the more serious condition related to their smoking habit and lung cancer, which is known to be exacerbated by smoking. Tar and other substances in cigarette smoke have damaging effects on the respiratory system, including destroying or paralyzing the cilia and causing an increase in mucus production, resulting in a persistent cough and susceptibility to respiratory ailments.