Detente, or the easing of tensions, became a major strategy in the 1970s. It was not new though, Eisenhower had started to attempt it after Stalin died in 1953.
Both countries started feeling the pressure of financing their military across the globe (though not enough to cause them to stop altogether). Detente was thus a way to reduce tensions and thus costs.
There was progress made under detente including by 1972 the Strategic Arms Limitations Talks (SALT) which was a decision between the two countries to not have certain types of weapons, and the Anti-Ballistic Missile Treaty which gave each country only 2 missile defence sites.
Nixon tried to make friends with both Red China and the Soviet Union under detente. It was well known by 1960 that they did not like each other, and Nixon hoped to play them off of one another.
Although detente was occurring, containment was simultaneously pursued. Things were not perfect, as the superpowers still posed a threat to each other, as shown in the Yom Kippur War.
Detente ceased when the Soviet Union invaded Afghanistan.