Why did Chancellor Palpatine reveal to Obi-Wan that Count Dooku was a Sith Lord?

Question

When Count Dooku enters the room in The Revenge of the Sith, Palpatine tries to dissuade his rescuers, Obi-Wan Kenobi and Anakin Skywalker, by revealing Count Dooku's true allegiance.

Chancellor Sheev Palpatine: Get help. You're no match for him. He's a Sith Lord.

Other than to make the two Jedi doubt themselves before an important duel, why would he reveal that?

Did he think the Jedi already know Count Dooku was a Sith Lord?

The events of the previous movie, The Attack of the Clones, could lead the Jedi to think of Dooku as Sith, but there's no confirmation of that in the movie. The Jedi could still think of Dooku as a former Jedi who turned dark because he didn't like the corruption in the Senate, but going dark is not the same as becoming a Sith Lord. They could also see him as somebody who led the Separatists because he had to defeat whatever Sith Lord controlled the Senate.

Is there anything in novels or the cartoon TV series where Dooku reveals such information to the Jedi, the public, or others?

Wouldn't revealing Dooku's status also reveal that Palpatine has access to Sith knowledge?

The Sith Lords were secretive. They don't advertise their status, and would reveal themselves to somebody they trusted, or somebody they could turn. Palpatine gave a clue to his own allegiance by revealing such knowledge to Obi-Wan and Anakin. One could not imagine a Sith Lord dropping such hints carelessly.

Answer 1

Here are the facts.

What drives Anakin to the dark side is his feelings about family, his mother and his wife, but also about his nonexistent father.

The Jedi Council came to the conclusion that the Sith still existed after Darth Maul revealed himself. They assumed that meant that there was another Sith out there because as Yoda says "Always two there are".

Darth Maul killed Qui Gon Jinn.

When Dooku talked to Obi Wan, he claimed that the Republic was under the control of Darth Sidious who had hundreds of senators under his sway.

After Palpatine tells Anakin that Dooku is a Sith Lord, Anakin kills Dooku even though Dooku has already been defeated and crippled.

Now here is the interpretation

First of all Palpatine wants to delay the discovery of his double identity until he is ready to make himself dictator. The ossified Jedi Council believes there can only be two Sith. Dooku was just as old as Palpatine and in the Clone Wars cartoon he had the habit of trying to take his own apprentices who the Jedi would encounter. He provides an extremely convenient answer to "Who was Maul's master". And if Dooku was the master, then Palpatine could not be the master. Suspicion allayed for now.

At the same time, the primary thing driving Anakin is his desire for family and his fear of loss of it. The death of his mother and his fear of the approaching death of his wife and his unborn offsping drive him to the dark side just as discovering he has a living son and seeing the Emperor torturing that son to death drives him away. But there is also the issue of Anakin's nonexistent daddy. Anakin wanted a father figure. Qui Gon could have been that father...but the Sith killed him. Very conveniently for Palpatine who can slip into the vacancy.

So when Anakin sees Palpatine abducted by Maul's presumptive master...he gets angry. The Sith killed his first "father". Maul was acting on his orders. The Sith threatened to do it again. So Anakin kills Dooku without need, in the heat of the moment with Sidious right there to infiltrate Anakin's mind in that vulnerable moment.

That's why he tells them that Dooku is Sith. It's not totally unbelievable that Dooku finally couldn't resist a little villain monologuing to his helpless enemy who he's about to kill. But the important thing is to make Anakin as angry as possible.

Answer 2

Palpatine tried to appear surprised and helpless, Jedi probably already knew

Jedi were 99% (if not full 100% ) certain that Dooku is a Sith Lord. Not just his lightsaber and use of Dark Side, but they found out in The Clone Wars, S6:E10 that he is a man called Tyranus that ordered Clone Army. There is also a comic with Quinlan Vos, where he hears the name Darth Tyranus. Also, Anakin and Obi-Wan met Dooku several times before this in various episodes of Clone Wars cartoon, therefore they already knew what to expect. Detailed answer on the question of Jedi knowledge about Dooku could be found here.

What about Palpatine ? Palpatine tries to keep his mask of being mild-mannered elderly statesmen, so he acts surprised as someone who who for the first time in his life realized that Sith actually do exist (Dooku told him: "Muahaha, I'm a Sith" :) ) and now wants to warn his friends. Throughout Clone Wars Palpatine downplays Sith threat, acts like they do not exist and at one point (Clone Wars S4:E22) explicitly forbids them to go searching for Maul and orders them to focus on war instead.

But now, his plans are nearing completion. Unknown to anyone except himself, he wants to lure Anakin to Dark Side, but also to get rid of Dooku. Therefore he reveals information that is essentially worthless, but psychologically triggers Anakin to use everything in the fight (including Dark Side) and feel no remorse to Doooku, to the point of killing him . More about Palpatine's psychological tricks here.

Finally, by admitting that Sith do exist, he sets up a situation for his latter conversations with Anakin, where Sith and power of Dark Side would become topic. Palpatine takes calculated risk, because his plan is to reveal himself as a Sith Lord to Anakin at some point. Therefore, he gently steers their relationship towards that.