Yep it's possible, you can create two customer tax classes under Sales->Tax->Manage Customer Tax Classes Let's call them Retail Customer and Trade Customer
Now Add Tax Rates under Sales->Tax->Manage Tax Rates, provide 0.00 for let's call them Tax Standard and Tax Zero
Now add Tax rules under Sales->Tax->Manage Tax Rules Tax Standard and Tax Zero You can then specify Tax Zero to be used with custom group Trade and Tax Standard to be used with retail.
You'll adjust general tax settings under System->configuration->Sales->Tax
Screenshot attached for reference.
