Should the US start negotiating with terrorist who take hostages, then make demands?

First rule of any negotiation: can you trust the person you are negotiating with to carry through with what they promise. Applies in just about any situation. Here, assuming the designation of terrorist is accurate and not political, then you can probably assume they can't be trusted.

Second rule: always be aware of the consequences of your actions, and the collateral effects of what you do. Once you start negotiating with terrorists, you send the message that you are willing to negotiate with terrorists. This gives them an incentive to continue taking hostages, since you have shown willingness before.

Let me put it another way. Negotiating with terrorists is like losing your virginity. Once you've done it, there's no going back.

FIRST US will have to find the terrorist and then only negotiations will be possible.Who are the terrorist? is not clear..individuals or a country or a communal group or only internal criminals and frustrated population?So,it needs strong vigilance and action rather blind attacks and genocides by US.

Of course not. Pretend to negotiate until the snipers are in place.

never, if you start that more and more hostages will be taken. just like in Mexico city, the kidnap capital of the world.

Absolutely NOT!

NO