38/38 Depends on the tire, try some different pressures and see what suits ya. The max pressure marked on the tire is just that; max pressure cold. Don't go beyond it.
I think Triumph recommends around 32-36, not quite sure, but that's just a starting point anyway.
Factors such as bike weight, rider weight, (I may be trying lower pressures

), passenger or no, luggage, etc., all affect the optimum pressure for your bike. Riding style factors in too.
I don't think I would go below 30 with these bikes regardless of tire.