Final answer:
Nixon promoted diplomatic relations with China to gain leverage in Vietnam War negotiations, exploit the Sino-Soviet split, and open up trade opportunities for the U.S.
Step-by-step explanation:
President Richard Nixon promoted a diplomatic relationship with China largely to gain strategical advantages during the Cold War. One of the pivotal reasons was to gain an advantage in negotiations to end the Vietnam War. By establishing a friendly relationship with China, Nixon aimed to isolate North Vietnam and secure peace terms that would allow the United States to withdraw from the war with honor. His diplomatic efforts led to China and the Soviet Union cautioning North Vietnam to use restraint, which was instrumental in bringing them to the negotiation table.
Another significant reason was to play the 'China card' against the Soviet Union, to prompt it to seek a better relationship with the United States and compete for global influence. By improving relations with China, the US was able to capitalize on the Sino-Soviet split and exert pressure on both China and the Soviet Union in its favor.
Moreover, this outreach to China was in part also a strategic move to open up trade opportunities for the United States. The potential economic benefits of engaging with the huge Chinese market were a considerable incentive for Nixon's administration.