There is an intriguing question regarding Rosh HaShanah. Why do we need both Rosh HaShanah and Yom Kippur; shouldn’t one day be enough? Why do we need to Daven on Rosh HaShanah, and then return to shul ten days later and Daven again? Also, Rosh HaShanah is the beginning of the Aseret Yimei Teshuvah, and if so, why are no Selichot or Vidui said on Rosh HaShanah?
A possible answer can be found in Masechet Rosh HaShanah (16b). The Gemara there says that the Tzadikim (righteous) are immediately written into the Sefer HaChayim, the Rishaim (evildoers) are immediately written into the Sefer HaMavet, and those in-between wait until Yom Kippur to be written into a Sefer. It seems from this Gemara that both Rosh HaShanah and Yom Kippur are needed, but this Gemara does not explain why.
An answer can be found when looking at the Mussaf of Rosh HaShanah. In this Mussaf, instead of simply reciting the Korban of the day like we usually do, we recite three paragraphs: Malchiot, Zichronot, and Shofarot. In these paragraphs we praise Hashem. In the first Berachah we use Hashem’s kingship to praise him, in the middle we refer to His compassion, and finally, in the third, we mention our blowing of the Shofar as an outlet to praise Hashem. Rosh HaShanah’s Mussaf differs significantly from the Mussaf of Yom Kippur. On Yom Kippur, instead of inserting these three special Brachot in our Davening, we in fact recite Selichot in the middle of Chazarat HaShatz.
The difference in the two Mussafim highlights the fundamental difference between the two days. On Rosh HaShanah, we ask for Teshuvah by using three Berachot of praise and hearing the 100 Kolot of the Shofar. On the other hand, we observe Yom Kippur by fasting and using a solemn attitude to beg Hashem for Teshuvah. We need the solemn attitude in order to ask for Teshuvah, yet at the same time, we also need to praise Hashem by demonstrating a happy attitude.
Rosh HaShanah is the real test for us. How do we approach Teshuvah when we are doing it through Ahavat Hashem (love of God) while we are eating and rejoicing? This is what distinguishes the righteous from the regular people and the wicked people. It is better to do Teshuvah through Ahavah as opposed to Yirah (fear). Therefore, the Tzadikim are able to beg for Teshuvah, despite the fact that they are in the midst of rejoicing. They are able to do Teshuvah solely out of love for Hashem. The Rishaim are not prepared even to give the Teshuvah elements any thought while they are busy celebrating, and therefore they are not even given until Yom Kippur. The bulk of the population are not able to completely atone for their sins. They are able, however, to show enough dedication to Teshuvah that the process can be deferred to Yom Kippur, despite the fact that it will be through Yirah. May we all have the peace of mind to be able to do a full Teshuvah on Rosh HaShanah and be immediately written into the book of life.