They use inverters to convert the DC to some square wave and approximate it to A/C using electronic gimmicks. Not a pure sine wave A/C, but close enough to run fans and the lamps. Energy conversion efficiency is not bad, the inverters do hot heat up too much. But they play havoc with the motors. So the Japanese A/C makers have been selling ruggadized air conditioners that can run on the inverter electricity.
The logical next step is to create A/C to run purely on DC. Probably it would use AC to DC converters to use grid electricity. Again this DC would be poor in quality compared to battery DC. So this Aircon also would need to be ruggadized.
All these calculations about when residential solar will become viable compared to coal or natural gas are completely different between G8 and rest of the world. Places like India will pay well over the current grid price for steady electricity supply. Not all of them. But the affluent population of India is about the size of Japan, some 120 million people. They have been making do with truck-battery-inverter contraptions, small gasoline generator sets etc. They would probably form the wave of early adopters who pay for the early fixed costs of solar panel factories.