A question about triac output of zero crossing SSR relay
The gate current comes from the load, and will be triggered near the zero crossing if it is to be on, so every 180°. 

There is no guarantee that there will be no DC component in the load current, if that is what you are asking, but it usually works out that way. If you were to pathologically provide pulses to the SSR timed to be near alternating zero crossings you could make it into a rectifier (for some, probably most, SSR designs). 



Edit: 


You should think of gate current, not gate voltage. In the example, the gate current will generally consist of spikes perhaps 100-200 microseconds long around the zero crossing. 
Zero cross switching is mostly for EMI reduction. If the device is switching infrequently, the EMI is less bothersome, as with mechanical relays. Of course the thyristor will not switch off until the current drops below the holding current (usually considered close to zero compared to the load current).