KarlKnechtel: This looks to me a lot harder than exercise 162 or 163, so I thought I'd give it a shot. I'm pretty sure this is correct:
looks odd, but seems to be an example of guzumi. White cannot yet atari Black's empty triangle on either side, due to damezumari - White must play at a first before b. And since would take the vital point of a bulky five, White has no time for this capturing plan - she must play herself, answering the empty triangle with one of her own.
That's the key; Black has now secured the bottom eye in sente (by threatening to make a second eye there), giving him time to complete the second eye at the top. makes miai of the c's and of the d's.
Later, White forces with Wa, Be, Wb, Bf. There is still lots of aji here! Note that Ba doesn't really help Black any, though it does give him one ko threat versus the several that White can get out of the position. is better than playing it at 3, even though it fails; the points available to Black are the same, and White gets more threats. I don't think I'm qualified to compare vs. tenuki, though.
xela: " is better than playing it at ": I disagree! It's a little tricky to count the territory in either case, because you have to remember that eventually black will be forced to capture the stones, and you have to reassure yourself that there's no under the stones traps here. In the above diagram, black will end up with 7 points of territory (one point below , and 6 points for capturing three white stones). If white plays at , then black will end up with 5 points of territory (two captives plus a point at f), and there's also potential for white to capture the stone next to . Generally, you'd take the extra two points rather than worrying about the number of threats in a hypothetical future ko.
Note that showing in the solution diagram is good, because you want to check that you've read out all the variations and can find if you need to. It's common that tsumego solutions show "the strongest resistance" rather than the moves you'd play in a real game.