This is a classic tesuji problem that appears for example in Lee Chang-ho’s collection of tesuji problems.
Black to play.
Solution
Failure Simply connecting at 1 does not cut it for Black. White extends his corner group’s liberties with 2, threatening to live with 3; if Black tries to prevent this with 3, then white 4 first captures Black.
Solution Black has to attack White’s corner liberties directly with 1–3. White has no choice but to capture with 4, after which Black forces 5–6 and . . .
Solution (contd.) . . . then throws in at 7 and 9, finally setting up a kō fight for the life of all three groups in the corner.
Solution added.