A spell or ability destroys a permanent only if that spell or ability specifically contains the word “destroy” in its text. If a spell or ability an opponent controls exiles a noncreature permanent you control, causes you to sacrifice a noncreature permanent, removes all loyalty counters from a planeswalker you control, or causes an ability you control to trigger (and then that ability destroys a permanent you control), Cobra Trap’s alternative cost condition hasn’t been met.

You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.

Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

Casting a Trap by paying its alternative cost doesn’t change its mana cost or mana value. The only difference is the cost you actually pay.