Final answer:
The Waters projection is the best radiographic view to demonstrate the maxillary sinuses, providing a clear, unobstructed image for examination.
Step-by-step explanation:
The radiographic projection that best demonstrates the maxillary sinuses is the Waters projection. This projection is specifically tailored for the visualisation of the maxillary sinuses without superimposition. The patient’s head is positioned with the chin touching the image receptor, and the nose approximately 1 to 2 inches away from the receptor. The central ray is directed perpendicular to the image receptor, which allows a clear view of the maxillary sinuses, making it the optimal choice for their examination.