Final answer:
The last formal declaration of war by the U.S. government was in World War II. Subsequent conflicts, such as in Korea and Vietnam, did not have formal declarations, instead being authorized by other means such as Congressional authorizations and UN resolutions.
Step-by-step explanation:
The last time the U.S. government formally declared war was during World War II. Following this conflict, the U.S. engaged in several significant military operations, such as the Korean War, Vietnam War, and the Gulf Wars. However, these were not preceded by a formal declaration of war but were authorized through Congressional authorizations to use force, United Nations resolutions, and sometimes NATO actions.
Several examples illustrate how the U.S. has managed to engage in conflicts without a declaration of war since World War II. This includes the War Powers Resolution passed in 1973, designed to reassert Congress's role in military decision-making, though it did not necessitate a formal declaration of war for military engagements.