So why don't they include two radars, one for sweeps and one for tracking? I know, I know, weight, power, etc. At the same time, isn't that the obvious answer?
Note how the radar's processing units and dish take up the entirety of the aircraft's nose and how large the system is compared to the technician working on it. There simply isn't enough space to add another radar.
Nor would it make sense to split that into two smaller radars, as the size of the dish and processing units is strongly linked to its power and range. That's one reason larger aircraft like the F-15, F-14 and Su-27 have longer-ranged and more powerful radars than smaller fighter aircraft.
Rather than having a mechanically-slaved reflective dish, an AESA radar has hundreds of Transmit/Receive Modules (TRMs) each capable of acting like a tiny radar dish by transmitting or receiving on its own frequency and being steered its own direction.
So now, rather than having the radar dish jump between track and scan at rapid intervals, the system can just dedicate a few hundred of the AESA TRMs to tracking one or more targets while letting the remainder continue sweeping the skies. There's no limitation on azimuth because each TRM can be individually steered.
So in short, the answer is that the latest fighter aircraft don't have two radars, they have hundreds or thousands of tiny radars that can work together in a whole bunch of useful combinations.
Edit: Replaced initial image with a Wiki Commons link that doesn't have linking issues.
It is important to note that the antennae in a phased array (TRMs) cannot be "steered" individually: it is the electronics that creates a beam by timing the transmit and receive signals to a number of antennae. It's similar to the way an array of atoms creates a pattern of beams in x-ray crystallography, if that makes it clearer.
This does also mean that the whole array can be pointed in multiple directions at once: The only limitation is the number of phase shifters coming off of each antenna (if the signals are directly sampled and then the beam forming is done in software you are then only limited by your processing power. I'm not sure if this is currently possible in radar but I've seen it done for sonar).
Yes, you're right, I shouldn't have simplified it that much. Upvoted you because your comment deserves more attention.
The steering uses amplitude and phase shifting to create beams through constructive or destructive interference. All very fascinating stuff, and it allows for additional uses like jamming and directional communications links.
as other commenter said ESA radars do great simultaneously scanning and tracking, with modern radars - more than 1 target simultaneously. The 2nd radar may be employed for the rear sphere like in that rear "stinger" http://www.airforceworld.com/bomber/eng/su34-fighter-bomber-...
How is it an obvious solution if it is not practical?
The electronically-scanned radars mentioned in the second answer can easily divide their time between the tasks (no mechanically-constrained dish to sweep) but there is definitely no space for two radar systems in the nose of a fighter.
