Yep it's possible, create two Customer tax class 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.
[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/cewHY.jpg