Daf Yomi - Sukkah 47 - Sukkah on Shmini Atzeres by Reb Jay

In chutz la'aretz, we sit in the sukka on Shemini Atzeres because of Sefika D'yoma, but we do not make a brocha (for this reason, on Leil Shemini Atzeres, we wait until it is tzeis hakochavim to make kiddush). Chasidim generally sit in the sukka only for kiddush during the day of Shemini Atzeres (Rav Tzadok Hakohen has a fifty page teshuva called Meishev Tzedek being matzdk this minhag). This is because of tartei d'sasrei, as there is a Midrash Tanchuma that asks how can we daven for rain (Tefilas Geshem is said on Shemini Atzeres), and then sit in the sukka (furthermore, the tartei d'sasrei is that two different Yomim Tovim are being celebrated--Sukkos and Shemini Atzeres). Maybe we can answer that even though it is a tartei d'sasrei, this paradox serves as a reminder that we are in galus, and galus itself, writes the Maharal (peirush to Shir Hashirim) is a stirah to the essence of Klal Yisroel.

Rav Ahron Kotler asks an interesting question. The chiyuv to sit in the sukka on Shemini Atzeres includes bein hashmashos as well. Why don't we say a person is patur from the sukka during bein hashmashos because of s'fek s'feika (perhaps today is sukkos, but even if it is, bein hashmashos itself is a time of safek, as to whether it is day or night)? He answers that bein hashmashos is not a safek but a zman bifnei atzmo.

The Sharey Teshuva mentions that there are opinions that say that if a person made a mistake during davening of Shemini Atzeres (only on the first day and only in chutz la'aretz and said "B'yom chag hasukkos hazeh" he is yotzei because the day while having a chelek of the kedusha of Shemini Atzeres, also has a chelek of sukkos, because of Sefika D'yoma.