מחק ברחמיך הרבים שטרי חובותינו…
On the Yomim Noraim we ask Hashem, in His mercy, to erase all of our spiritual debts. The Roshei Teivos of the tefillah spell out the word בשמחה , because it is only through joy that the decrees can be overturned.
– Parparos
The Vidui (confessions) recited on Yom Kippur are traditionally sung to a universal niggun. Why sing your confessions? Because even teshuvah needs to be done b’simcha and with love. When you return out of love, your transgressions are transformed into mitzvos. — Tiferes Yisroel
True simcha comes through Torah. Where do we see this? On Sukkos, the holiday of simcha, we shake the 4 species bundled together. The gematria of אתרג is 610, plus the 3 other species, equals 613, the number of
mitzvos in the Torah. — Anaf Yosef B’shem HaMedrash
Why are we so happy on Simchas Torah? It’s not because we have completed the Torah, but because we are beginning it anew. — Chiddushei HaRim
Someone once asked why there is no tefillah on Rosh Hashanah for happiness. Simcha is a choice, a state of mind. The word בשמחה (happiness) has the same letters as מחשבה (thought).