Final answer:
King Louis XIV portrayed the Sun King in the ballet 'Le Ballet de la Nuit.' None of the options provided in the question are accurate. His performance epitomized royal splendor and helped advance ballet as a high art form.
Step-by-step explanation:
King Louis XIV performed in the ballet titled Le Ballet de la Nuit (The Ballet of the Night), and in this production, he famously portrayed the role of the Sun King, which reinforced his image as a powerful, central figure of the French monarchy, much like the sun is the central body in the solar system.
This performance took place long before the ballets Swan Lake, The Nutcracker, The Sleeping Beauty, and Giselle were composed. It is well-documented that Louis XIV's performances and his patronage of the arts played a significant role in the development of ballet as a serious art form.
Notably, the grandeur and majesty of the King were reflected in the elaborate cultural events that took place at the Palace of Versailles, from ballets and balls to hunts and receptions, establishing Versailles as the cultural heart of France.