Do not have low beams - 2003 Toyota Corolla

Did you test the low beam electrical circuit using a volt meter ? Look at a wiring diagram to see what all is involved in turning the lights on ? Do you know how to test electrical circuits ?
Also reading service repair manual about the head lamps opp. would be a good thing to do .
Headlamps
The major common components of this system are the body control module (BCM), ambient light sensor, multifunction switch, park brake switch, and the headlamps.
The headlamps may be turned on in 2 different ways. First, when the driver places the headlamp switch in the HEADLAMP position, normal operation occurs. Second, with the headlamp switch is placed in the AUTO position, automatic lamp control (ALC) occurs. During ALC control, the headlamps will be in daytime running lamp (DRL) operation in daylight conditions, or low beam operation in low light conditions.
The low beam relay and high beam relay receive battery positive voltage directly from the battery through the HDM and COILS fuses in the underhood fuse block. The BCM supplies a ground signal to the low beam relay coil for automatic headlamp control and normal headlamp operation. The BCM also supplies ground to the high beam relay coil for high beam headlamp operation. When the driver places the headlamp switch in the HEADLAMP position and the dimmer switch is in the low beam position, the low beam relay energizes sending current flow through the left and right low beam headlamp fuses to both low beam headlamps. The dimmer switch sends a ground signal to the BCM in the high beam position and a momentary ground signal in the flash-to-Pass (FTP) position from G102 to deactivate the low beam headlights and activate the high beam headlights. With the headlights in the low beam position, the high beams may be momentarily turned on or flashed by activating the FTP portion of the switch.

Low Beams - Standard
The standard low beam headlamps receive voltage from the headlamp driver module located in the underhood fuse block. The body control module (BCM) controls the headlamp driver module with the headlamp low beam relay control circuit. Low beam control is determined by a signal on the headlamp dimmer switch signal circuit from the multifunction switch. When the headlamps are requested ON and the headlamp dimmer switch signal circuit is open, the BCM sends a pulse width modulated (PWM) ground signal though the headlamp low beam relay control circuit to the headlamp driver module which illuminates the low beam headlamps at a 100 percent intensity level. The right and left low beam circuits are independent and are fused separately in the underhood fuse block. The LOW HDLP-RT 10A fuse supplies voltage to the right low beam headlamp and the LOW HDLP-LT 10A fuse supplies voltage to the left low beam headlamp. The right and left headlamps are grounded at G103 and G107 respectively.

Your best bet mite be to have a qualified technician check it

Maybe a problem with dimmer switch? You have lo beam fuses and low beam relay in under hood fuse box, use a test light, check for voltage at the lo beam fuses with lo beams turned on. I wouldn't think both right and left lo beam fuses would blow at the same time.
The bcm grounds the lo beam relay. The dimmer switch lets the bcm know what's going on, so the bcm will ground the lo beam relay.
I can only help with testing. I looked at info for Silverado.

On the inside of the lid is a diagram .
The headlamps may be turned ON 2 different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the AUTO position, for automatic lamp control (ALC). During ALC, the headlamps will be OFF in daylight conditions, or low beam operation in low light conditions. Battery positive voltage is supplied to the low beam relay and the high beam relay in the underhood fuse block. When low beam headlamps are requested, the body control module (BCM) supplies ground to the coil side of the low beam relay. This activates the relay and the relay supplies voltage to the left hand low beam headlamp through the LH LOW BEAM fuse and to the right hand low beam headlamp through the RH LOW BEAM fuse. Ground for the left hand low beam headlamp is provided at G101. Ground for the right hand low beam headlamp is provided at G102. When high beam headlamps are requested, the body control module (BCM) supplies ground to the coil side of the high beam relay. This activates the relay and the relay supplies voltage to the left hand high beam headlamp through the LH HIGH BEAM fuse and to the right hand high beam headlamp through the RH HIGH BEAM fuse. Ground for the left hand high beam headlamp is provided at G101. Ground for the right hand high beam headlamp is provided at G102.

Which do you have
Low Beams - High Intensity Discharge (HID) OR
Low Beams - Standard ?

The low beam headlamps receive voltage from the headlamp low beam relay located in the underhood fuse block. The BCM controls the relay on the headlamp low beam relay control circuit. Low beam control is determined by a signal on the headlamp dimmer switch signal circuit from the multifunction switch. When the headlamp dimmer switch signal circuit is open, the BCM grounds the headlamp low beam relay control circuit, illuminating the low beam headlamps. The right and left low beam circuits are independent are fused independently in the underhood fuse block. I suggest you take an have it diagnosed by an ASE certified repair shop that has a scan tool that can communicate with the BCM .
DTC B2575 00: Headlamp Control Circuit

I would check for the groundwire continuity

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First check light relay fuse, if ok check battery voltage at low beam light terminal, if ok replace low beam bulb, if no voltage check switch side of relay, if voltage replace relay, if no voltage check headlight low beam switch.

It can be faulty low beam lamp or its connection issue for low beam lamps.

There are few solved helps links with proper solution to troubleshoot these issues.I suggest you to refer the links below.Click the link:----
Passenger side low beam out?

http://repairhelpcenter.blogspot.com/2012/01/passenger-side-low-beam-out.html

------------
Low beam HID light goes out? http://schematicsdiagram.blogspot.com/2012/01/low-beam-hid-light-goes-out.html
----------2007 Dodge Caliber: Low Beam Headlight Not working http://technoanswers.blogspot.in/2012/06/2007-dodge-caliber-low-beam-headlight.html
-------------Chevy Tahoe: Low Beam Lamps are not working? http://technoanswers.blogspot.in/2012/04/chevy-tahoe-low-beam-lamps-are-not.html
----------2001 Chevrolet Tahoe: Both Low Beam Lamps Not Working? http://technoanswers.blogspot.in/2012/04/2001-chevrolet-tahoe-both-low-beam.html
--------------2002 Toyota Tacoma: Low Beams not working? http://technoanswers.blogspot.in/2012/04/2002-toyota-tacoma-low-beams-not.html
-----------Low beam headlights Modification? http://schematicsdiagram.blogspot.in/2012/04/low-beam-headlights-modification.html
-----------DRL and Low beams not working? http://schematicsdiagram.blogspot.in/2012/04/drl-and-low-beams-not-working.html
-----------These will help.Thanks.

These trucks are known for bad multifuction switches.
the switch that i talk of is the signal switch , the handle is the switch, it bolts to side of steering column . this switch controls the signals and the headlights and high /low beams. the other thing is the headlight switch connector, the connector some times goes bad and starts to melt or just comes out of the connector. you will need to remove the cover to steering column, the screws are located under the bottom cover in holes. remove cover and check connector and then test for power if you have power going into switch but not coming out then switch is bad.

the last thing is to make sure the bulbs are good , make sure the headlight bulbs are good , and also the driving light bulbs, test for power at the connectors to those lights to.
You will need to do a little testing to find the problem.

low beams are on with the high beams does NOT mean the bulbs are good. The low beams have two separate filaments, one that lights on low beam and one that lights on high beam. That's why the low beams have three terminals but the high beams have only two.It's entirely possible that both low beam filaments have burned out. If the bulbs really are good, then the dimmer switch is the most likely problem.

DID YOU CHECK THE BULBS?