Are you considering this plane stress? If you are, you'll have two principal stresses. Think about Mohr's Circle for a second...The principal stresses lie in a plane with no shear stresses (they lie on the horizontal axis). So if you rotate around 90° in Mohr's circle, you'll get to the point of max shear (the highest point on the vertical axis). Geometrically speaking that is the same as saying
[tex]\tau_{max} = \frac{\sigma_1\sigma_2}{2}[/tex]
This also assumes that you follow the standard practice of numbering the highest principal stress as [tex]\sigma_1[/tex].
You can double check it by running the calculation with the regular stress components:
[tex]\tau_{max}=\sqrt{\left[ \frac{\sigma_x\sigma_y}{2}\right]^2 + \tau_{xy}^2}[/tex]
