Responsa for Rosh Hashanah 68:7
מ"ט אמר רבה אמר הקב"ה אמרו לפני בר"ה מלכיות זכרונות ושופרות מלכיות כדי שתמליכוני עליכם זכרונות כדי שיבא לפני זכרוניכם לטובה ובמה בשופר:
IF ONE HAS SAID THE [NINE] BLESSINGS AND THEN PROCURES A SHOFAR, HE SOUNDS A TEKI'AH, TERU'AH, TEKI'AH. The reason is that he had no shofar to begin with. This shows that if he had a shofar to begin with, when he hears the blasts he must hear them during the recital of the blessings.<span class="x" onmousemove="('comment',' V. supra 32a.');"><sup>9</sup></span>
Shut min haShamayim
They responded: "How pious are these generations!" (Yevamot 39b:15) "All that Sarah says to you, listen to her voice!" (Genesis 21:12) "Go and say to them, return to your tents and bless your God!" (Deuteronomy 5:27, Nehemiah 9:5) The proof is from Channukah candles and megillah reading. They explained to me that just as in these cases, since the women were involved in the original miracle they are obligated to perform the commandment and recite the blessing, so too with the Lulav, we find that the [entire] Jewish people have only one heart directed to their Father in heaven (Sukkah 45b.9). So too with the Shofar, we are taught that the Holy One said: bring me [verses of] kingship, that I may be your king, and [verses of] remembrance, that the memory of your ancestors come before Me favourably, and all of that, with a Shofar. (Rosh Hashanah 34b.7) Now, women also need to be remembered before Him favourably. Therefore, if they recite the blessings for these commandments, they have permission to do so.*This is also the opinion of Rabbeinu Tam, quoted in Tosafot on Rosh Hashanah 33a:5
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