Option 1 states that extensive deserts occur in the western tropical regions of continents because of easterly trade winds. However, easterly trade winds blow from east to west, so they would not be the cause of deserts in western regions.

Option 2 suggests that cold ocean currents along western coasts result in extensive deserts. This is not entirely accurate as cold ocean currents can actually have a moderating effect on the climate, making it cooler and more humid, rather than creating deserts.

Option 3 correctly explains that the effect of both offshore easterly trade winds and cold ocean currents leads to the occurrence of extensive deserts in western tropical regions. The combination of these two factors can create conditions that are dry and arid, leading to the formation of deserts.

Option 4 suggests that the rate of evaporation is greater along the western margin areas, leading to the formation of deserts. While evaporation can play a role in creating aridity, it is not the sole factor responsible for the extensive deserts in these regions.

Overall, option 3 provides the most accurate explanation for the occurrence of extensive deserts in western tropical regions of continents.