Why do we use delta_star connection to drive electrical motors?

To reduce starting current 3-4 times than full load current and to increase the starting torque

To lower the starting current of motor.Motor first start in star connection .

When high starting torque is required along with a constant running speed in an application,  star-delta connection of motor is applied. But not delta-star connection is applicable in motor control.  

star and delta is the two basic three phase connection. when you need more current and a neutral point then star connection is practiced but when high voltage is concerned then delta is used. for star connection line currents are equal to phase current and line voltage is root 3 times of phase voltage as for delta connection phase voltage is equal to line voltage but line current is root 3 times of phase current.

minimaz the line voltage thus line current with low tourqe in starting 

To decrease the starting current when the motor starts its operation.

to mimimize line voltage thus line currect with low torque in starting and inrush to the sytem....then switch to delta as normal running...