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).
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.
[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?