How did President Reagan's approach to defense change the Cold War?
Regan's approach to changing the scope and momentum in the Cold War was to drive American military spending to such a level that it would eventually wear out the Soviet Union. Banking on the prosperity of the United States during the 1980s, Reagan calculated that spending on military initiatives such as personnel growth and SDI (as described below) would tax out the Soviet Union and ensure they would capitulate because of the inability to compete. To a certain extent, he was correct, as the Soviet Union possessed a level of fear about SDI and the growth of the American military presence. At the same time, Reagan was able to develop channels of persuasion through the Soviet Leader Gorbachev to deescalate Cold War tensions. The presence of Gorbachev almost had as much to do with Reagan's approach to changing the dynamic of the Cold War as much as anything else.
I suppose that you can say that Ronald Reagan's more aggressive approach to defense during his two terms in office helped to cause the Soviet Union to collapse.
When Reagan came into office, he increased defense spending and started in on things like the Strategic Defense Initiative (aka Star Wars). You can argue that doing this undermined the Soviet Union.
What happened is that the Soviet Union had to increase its spending to keep up with the US. But the Soviets weren't as rich as the US and so this added spending ruined them and that led to the downfall of the Soviet Union and the end of the Cold War.