Final answer:
The best treatment option is giving donepezil in the morning and adding trazodone at night. Donepezil slows the progression of Alzheimer's disease, while trazodone can improve sleep quality and address the patient's sleeping issues and low mood.
Step-by-step explanation:
The best treatment option for the 72-year-old woman with Alzheimer's disease who is experiencing sleeping troubles is Option D: Giving donepezil in the morning and adding trazodone at night. Donepezil is a cholinesterase inhibitor that helps slow the progression of Alzheimer's disease by enhancing communication between neurons. Trazodone is an antidepressant that also has sedative effects and can help improve sleep quality. Both medications can help address the patient's sleeping issues, low mood, and nighttime agitation.