4 of 4 Clarifying reformulation. Extra question.

What is this alternate cut after 3-3 against double keima round hoshi?

In 38 Basic Joseki, Kosugi & Davies remark in this position:

$$c
$$ --------------------
$$ -. . . . . . . . . .
$$ -. . . . . . . . . .
$$ -. . 1 . . O . . . .
$$ -. . . X . a . . . X
$$ -. . . 3 2 6 . . . .
$$ -. . O 4 5 . . . . .
$$ -. . . . 7 . . . . .
$$ -. . . . . . . . . .
$$ -. . . . . . . . . .
$$ -. . . X . . . . . ,

that if White blocks at 2, Black will push and cut with 3 and 5 or 3 and a.

I cannot see how one is meant to cut with 3 and a in this situation. I have not found this in Ishida, or on Josekipedia (though someone has asked a question about a) or in Sensei’s Library; though with this severely pruned search pattern (only shaded points sought):

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there were some matches (to which the “a” refers), but nothing useful that I could see.

Questions

  • Is this a misprint, or how is one meant to cut with 3 and a?
  • When is this preferable?
  • What continuations are there, and are they joseki?

Follow-up

I am not sure what I can have thought (though I expected a to be an answer to a different White 4, rather than achieving a different objective), but now I think I see, as Daniel T says in his answer that the marked white stones are separated:

$$c
$$ --------------------
$$ -. . . . . . . . . .
$$ -. . . . . . . . . .
$$ -. . X . c W . . . .
$$ -. . . X b B . . . X
$$ -. . . X W d . . . .
$$ -. . O O a . . . . .
$$ -. . . . . . . . . .
$$ -. . . . . . . . . .
$$ -. . . . . . . . . .
$$ -. . . X . . . . . ,

He shows W@a–B@b, but W b and d also seem to fail, with a shaky ladder and too many cuts respectively. I still do not see when this is good; maybe the issue is which 6-3 stone B wants to separate 5-5 from, but he could just push 3 in the other direction.