Solution (1) If White gets to play at 1, no combination of two black moves can kill his group, and so we can quickly figure out that black 1 is the only possible starting move. If White challenges Black with 2, black 3 and on ensure that White cannot win a local capturing race.
Black is tricked White 2 in this diagram is arguably the trickier white resistance. Black has to be careful not to play the atari of 5, as, after white 6, there is no way for Black to capture White unconditionally.
Solution (2) After white 4, it is correct for Black to simply connect with 5. After white 6, Black can then prevent White from getting a second eye in the corner with 7–13. White can try to be even trickier and play 10 instead of 6, trying to goad Black into another kō fight with black 6 and white 8. However, Black can then instead play directly at 8 to avoid the kō.
Solution added.