Reb Moshe Chaim of Slonim zt'l would tell people who were excessively afraid of the Yomim Norai'm, "It isn't a band of thieves who sit in the Heavenly court. It is our Father, and we can trust He will save His children."
There was a bachur who was terrified of the judgment of Rosh Hashanah. The Chazon Ish zt'l asked the bachur, "Why don't we say Tashlich when Rosh Hashanah falls on Shabbos?" The bachur repeated the reason written in the Mishnah Berurah (583:8). It is because people carry their machzorim to Tashlich, and on Shabbos, one isn’t permitted to carry.
The Chazon Ish told the bachur, "For you, the problem isn't only carrying the machzor. You are also carrying your sins because I see you're carrying a heavy burden on your shoulders." In this witty way, the Chazon Ish taught this bachur the proper Rosh Hashanah attitude.
Sadness draws strict judgment on oneself. Therefore, according to the Chasam Sofer, it is important to be happy on Rosh Hashanah, and then we will be judged with compassion and mercy.
Tur (581) states, "The way of the world is that on a day of judgment, a person dresses in dark clothes, doesn’t shave, and doesn't cut his fingernails because he doesn't know what the outcome of the judgment will be, but not the Jewish nation. They dress in white and cut their nails [on erev Rosh Hashanah]; they eat, drink, and are happy on Rosh Hashanah because they are certain that Hakadosh Baruch Hu will perform miracles for them. Therefore, the custom is to take a haircut, launder one’s clothing, and prepare good foods in honor of Rosh Hashanah."
It states (Tehilim 96:11-13) ...הארץ ותגל השמים ישמחו הארץ לשפוט בא כי 'ה לפני, "The heavens will rejoice, and the earth will exult...before Hashem for He has come to judge the earth." The Meiri (Chibur haTeshuvah 2:7) proves from this pasuk that we must be happy on Rosh Hashanah because Hashem judges the earth on this day, and we merit to be in His presence.
As is known, Hashem's name ה"הוי can be spelled twelve different ways, corresponding to the twelve months. Each month has another formation of Hashem’s name ה"הוי. The formation for Tishrei is ה"והי. The Magen Avraham (of Trisk) zt’l explains that this is because Chazal teach us that והיה represents joy, and we should be happy this month. Our happiness isn't limited to the yom tov of Succos but begins on Rosh Hashanah and continues in Aseres Yemei Teshuvah and Yom Kippur.
The Siforno (Vayikra 23:24) writes, "Although on this day, Hashem sits on His throne of judgment, it is proper that we rejoice because He is our King, and He will seek to do kindness and judge us favorably. As it states, יושעינו הוא מלכנו 'ה מחוקקנו 'ה שופטנו 'ה כי, 'Hashem is our judge, Hashem is our King, and He will help us.'"
The Chasam Sofer (Drashos) writes, "Rosh Hashanah is an awesome and fearful day. It is a day of judgment for the entire world. However, it isn't a sad day. It is a joyous day, the joy of teshuvah, ahavah, and deveikus..."
The Avodas Yisrael (Netzavim) writes, "Teshuvah must be performed with joy. One must have bitachon that Hashem won't abandon His nation. We don't say tachanun on erev Rosh Hashanah, maybe to hint to us that we don't need to fall on our faces. Rather, we should stand before Hashem with love and joy."
The Chinuch (311) writes, "Hashem performs kindness with His creations and reviews their deeds one day each year [on Rosh Hashanah] before their sins become too many. Their sins are still few, so Hashem forgives them. If He would only review their deeds once in a very long time, their sins would be many, and the world may be destroyed, chalilah. Rosh Hashanah, therefore, is a very special day. The world's existence is dependent on this day. It is proper to make this day a yom tov. It is among the special yomim tovim of the year."
The Chinuch (311) writes, "Despite our joy, it is a day of judgment, so it is appropriate that we be afraid. This is why we don’t say Hallel on this holiday. It isn’t proper to sing Hallel while standing in judgment."
Shulchan Aruch (597:1) states, "We eat, drink, and are happy, and we don't fast on Rosh Hashanah. However, one shouldn't eat until he is full so that he won't have ראש קלות, lightheadedness on Rosh Hashanah, and he will have the fear of Hashem on his face." This perfectly expresses the spirit of the day. We are happy, but not lightheaded, chalilah. Fear of heaven should always be on our faces. Rosh Hashanah is a day of conflicting emotions because we experience fear and joy on this day. We stand in judgment, so we are afraid, but we are also happy and confident that Hashem will find a way to acquit us and grant us a good year.
The Mishnah Berurah explains, "Although Rosh Hashanah is the day of judgment, nevertheless, the mitzvah of בחגך ושמחת, to be happy on yom tov, applies to Rosh Hashanah, too, because Rosh Hashanah is called a chag, as it states (Tehillim 81:4) חגנו ליום בבסה, and it states in Nechemiah (8:10, regarding Rosh Hashanah) ואתה ,לאדנינו היום קדוש כי ...ממתקים ושתו משמנים אכלו מעוזכם היא 'ה חדות כי תעצבו אל, 'Go, eat fat foods and drink sweet drinks...for the day is holy to Hashem. Do not be sad, for the joy...is your strength.'"
The Maharil writes that the first day of Rosh Hashanah is קשיא דינא, severe dinim. The second day is רפיא דינא, a softer judgment. The Shaul u’Meishiv (ה"קכ ג"ח רביעא מהדורה) disagrees. He writes, "This idea that the first day is קשיא דינא is difficult to understand because there are proofs that it isn’t a harsh day at all. The halachah is that we say shehechiyanu on this day. We wouldn’t say shehechiyanu if it weren’t a day of joy. (We don’t say shehechiyanu during sefiras ha’omer due to the churban Beis HaMikdash.) Therefore, it isn’t דינא קשיא. It’s a day when Hashem forgives our sins; it is a holy day. On this day, the imahos were remembered [to bear children], and all goodness and holy bounty comes from this day."
The Mishnah Berurah (584:1) writes, "We don't say Hallel on Rosh Hashanah because the books of life and death are opened, so how can we sing? Although we are certain we will be acquitted and found innocent in the judgment, one must be afraid due to the awe of the judgment. In the merit of his fear, he will be remembered [for a good year]."
