Question

Why are there three different wind patterns in each hemisphere

Answer 1

Well the answer is  tropics are hot . when its hot , hot air rises . The poles are cold. when its cold, the air sinks.The  Coriolis effect of the earth's rotation, perhaps that the air rising between the tropics would move to the poles before sinking but since it spins to the right in the northern hemisphere ,and to the left in the southern, it forms those two belts of high pressures at roughly the latitudes 30 N and 30 S as described in the image from Venkata, here above. Which in this case it  forms the Hadley cell.