I STRONGLY agree with Schmarmpit above. It's asking for a house-fire.
I had a similar problem, albeit with a fan heater (loft grow in winter) and a 600w set-up. Here's the problem and solution.
I am guessing the breaker trips at lights-on time, then trips again when you try and re-set it. This is because of the sudden current draw required by the ballast to ignite the lamp, which is far more than the normal running current. It's the reason we use contactors to stop this surge blowing timers.
Now, a 15A circuit will handle this current draw, and it will handle the A/C unit, just not at the same time.
So the solution is to have the a/c on a timer set to turn off while the lamp fires up, then turn back on again.
Assuming your lights and a/c are on timers, it's also advisable to check they stay in sync every couple of weeks. Mine drift about a minute a month.
My final piece of advice is to ensure extension cords are fully extended and not coiled up (coiled leads have a lower current carrying capacity). Shorten them if necessary.