Trashing two birds with one stone

Question

If I have a card that I have to trash another card to use, can I trash a card that has a paid ability where the cost is to trash the card, and then activate the paid ability?

Consider Trade-In and Cortez Chip (emphasis mine).

Trade-In:

As an additional cost to play this event, trash an installed piece of hardware. Gain credits equal to half the install cost of the trashed hardware (rounded down) and search your stack for a piece of hardware, reveal it, and add it to your grip. Shuffle your stack.

Cortez Chip:

[Trash]: Choose a piece of ice. The Corp must pay 2[Credits] as an additional cost to rez that ice until the end of the turn.

Assuming I had a Cortez Chip in play, could I play Trade-In and trash Cortez Chip, and use the effects of both cards?

Answer 1

No. Once the first paid ability is triggered, it resolves completely before another paid ability can be triggered. The exceptions are "prevent" and "avoid" abilities. So, in your example either ability will result in the Cortez Chip being in the Heap and no longer installed before you could possibly trigger the other ability. The specific text from the rulebook that applies:

Once an ability is triggered, its effect is resolved immediately and can only be stopped by prevent or avoid effects.