Trumpeting Carnosaur

A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.

When you discover, you must exile cards. The only optional part of the ability is whether you cast the exiled card or put it into your hand.

If you cast a spell "without paying its mana cost", you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the spell has any mandatory additional costs, you must pay those to cast it.