Remember that the monsoons are driven by differential heating of land and water. In the case of the summer monsoon, strong summer radiation creates very low pressure over land. High pressure forms over the ocean, because it does not warm as rapidly as land. Consequently, moisture-laden winds flow onto the continent. The winter monsoon is just the opposite.
High pressure forms over land due to weaker winter radiation.
Low pressure develops over the ocean. And, dry winds flow from the continent to the ocean. Changing seasonal insolation will change the strength of the monsoons. Stronger summer radiation will strengthen the summer monsoon. Weaker winter radiation will strengthen the winter monsoon.