三角比を含む等式証明問題です。どうすればいいかわかりません。詳しく解説お願いします。

1 | J sinx + cosxt tan のとき 5+2√√3 √3 Cosetsinet tan x 573 2√3

数列です

5 OKAKIYOSHIの10文字を、 次の制限を付けて並べるとき, それぞれ何通りの並べ方が あるか. (1) 子音の位置は OKAKIYOSHIのままとする。 e) 子音は左から KKYSH の順にある. SETJIRA ZAJNAHEL (2) AÐÅÄËJJRJD

この問題の答えを教えてください🙏

【ⅢI】 次の(A), (B)の設問に答えよ。 (A)14点,(B) 6点) (A) 次の英文を読んで下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は, アイウエオ順に解答すること｡ Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Mo Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really ( 1 ) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. B(A) Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: (2) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex (4) (6) -11-

この問題の答えを教えてください🙇‍♀️

【Ⅲ】 次の(A), (B)の設問に答えよ。 ((A)14点,(B)6点) (A) 次の英文を読んで,下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は、 アイウエオ順に解答すること。 Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Hot Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really (1) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more. because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. ant mo Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have to take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: ( 2 ) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex ( 4 ) (6) -11- 18

至急です。なぜ、逆関数ではx＝tanyが成り立つのでしょうか。解説出来る方、お願いします。

= (²+¹) ² 19 139 種々の関数の導関数, 第2次導関数 (0<x< 1/7) y=tan.x で表せ。 [2]x=3t, y=9t+1 のとき, き x=tany すことができる。 d'y d/dy (2) dx² OLUTION CGEART OS (1) 高校数学の範囲では, y = tanx の逆関数は求められないが, y=g(x) のと dy 101 dx dx を利用すると,g(x) をxの式で表 dy 10<x<1のとき dxdx 172/6, J37 であることから, ゆえにg'(x)= dx-9t², 2=91², (2) dt (dx)=- の逆関数を y=g(x) とするとき, g'(x) をxの式 D tanx>0 dy_1 dx cos2y=- == d (dy dt dt dx dx よって, y=g(x) において, x>0,0<y</であり、 80 x=tany が成り立つ。 (x) dx dy d'y dx² dx dx d'y dx2 dy=9 であるから dt 1 cos2y d - d (dx)= a (2) = dx dt 1/ ( 7 ) . dt to dx 1+tany 1+x² をtの式で表せ。 dy dx 2 7/13 - 1²/2=-275 9t² 9t5 (iniai+1200)n-z] を利用。 1 97² = 7/2 2 xd- KO+x+x) | 基本 124,138 f(x)=tanx とすると g ¹(x)=f(x) y=g(x) において x=g(y)=f(y) =tany I ↓ (2) la は d²y | d (12) dx2 ないことに注意する。 dy dx SET dt dx をxで微分。 合成関数の微分。 13 (0) 1 dx dt では 217 5

（2）のだ液の働きによって〜がいくつかつながった物質に分解されたことが分かるのところの①②③に当てはまる言葉を教えてほしいです 写真見にくくてすみません

1 実験 Ⅰ だ液のはたらきについて調べるために、次の実験を行った。 あとの問いに答えよ。 4本の試験管A~Dにデンプンのりを10cmずつ入れ, AとCには水でうすめただ液を, BとDには水をそれ ぞれ2cmずつ加え, 図1のように40℃の湯につけた。 10分後、図2のようにAとBにはヨウ素液を、CとDにはベネジクト液を加えて加熱し, 反応を調べたとこ ろ、表のような結果になった。 図 1 前チェック問題2] ⅡI -... ABCDacter 試験管A… デンプンのり+ だ液 試験管B… デンプンのり+水 試験管C･デンプンのり+ だ液 試験管D… デンプンのり+水 3 1 図2 表 A B ヨウ素液 ヨウ素液 ベネジクト液 (2) 次の文の ① ③にあてはまる物質名を書け。 実験の結果から,だ液のはたらきによって ① ++R$3040 St D set □(1) 試験管Cでは、ベネジクト液によってどのような反応が起きたか。次のア~エから1つ選べ。 ア 青紫色に変化した。 白くにごった。 気体が発生した。 エ 赤褐色の沈殿が生じた。 ARON ベネジクト液 沸とう石 デンプンのり + だ液 (試験管A) 反応なし (試験管C) 反応あり デンプンのり+水 (試験管B) 反応あり (試験管D) 反応なし 16 ② がいくつかつながった物質)に分解されたことがわかる。 I Stic318A LOAD など ARE

この問題の答えが「cannot(can't) be」なのですが、「~であるはずだ」はshould ではないのですか？ こういった例外の場合、どのように見分ければいいか教えて欲しいです🙏

BOV raib en iw uoy glen 1 Hare (0) Fill in each blank with suitable words to complete the sentence. ant juo ise ow 16/2" (8) (1) これが今年最高の映画であるはずがない。 STUS129) srittis eldste beviset bluoria eW [X] the best movie of This the year.

答えが配られず復習ができないのでどなたか教えていただけないでしょうか？😿

④ 各組に共通して入る語を答えよ。与えられた文字で始めること。Low( 1. (a) The two roads (j 3. (b) Start eating, please. I'll (j 4. 2. (a) Don't get so upset. I didn't (m 心を乱すすめす suryning back to bandwarat gniony@o rdiny, soy deal avaasi air to yoam belial adole 4- 語・イディオム ] )nigsd 2.55) ) here. ) you in a few minutes. ) it. (b) Everybody hates her because she is always ( m TO 20 DE (a) We'd like to see him some (o (b) Could you turn it the (0 Quods ) time. ) way around? veborit blari \ o (a) I hate big banks because they make you wait for your (t (b) How can you (t ) your back on me now? the latter 5. (a) You must forget the past and start li (b) The committee will (p Okenn ( 活水女子大) ) to them. ai\ og au\smb) JI 2点 of me in public. (国士舘大) (p living in the ) its final report to Parliament in April. (駒澤大) ( 東京理科大) site) ai is d ). dustrial proc We're friends, aren't we? M coeping vid \ned) STAT .). (明治大) (R) 17

３の問題と、⑺の和訳が分かりません。 ⑺は、二人の旧友が長い間会わずして再会して、彼らは何時間も話し込んだ。 この訳し方でいいんですかね?

【1】 教科書 P.82~86 Reading “Table for Two " の前半部分を読んで設問に答えなさい。 In 1947, (1) my mother, Deborah, was a twenty one year-old student at New York University, majoring in English literature. She was a beautiful woman with a great passion for books and ideas, who read hungrily and hoped to become a writer one day. (2) My father, Joseph, was a budding painter who supported himself by teaching art at a junior high school in New York. On Saturdays, he would paint all day, either at home or in Central Park, and eat out for dinner. (3) One Saturday night, he chose a neighborhood restaurant called the Milky Way. The Milky Way happened to be my mother's favorite restaurant. On that Saturday, after studying throughout the morning and early afternoon, (4) she went there for dinner. carrying along a used copy of Dickens' novel, Great Expectations. The restaurant was crowded, and she was given a table in a corner. She settled in for an evening of nice food, red wine, and Dickens. Within half an hour, all the tables were taken. (5) The waiter came over and asked my mother if she would share her table with someone else. Without looking up from her book, my mother agreed. “A tragic life for poor dear Pip," my father said, mentioning the hero's name when he saw the torn cover of Great Expectations. My mother absently looked up at him, and at that moment, she saw something strangely familiar in his eyes. Actually, she saw herself in his eyes. My father, entirely charmed with the woman before him, swears to this day that he heard a voice inside his head. “She is your destiny," the voice said, and immediately after that, he felt a sweet sensation running from the tips of his toes to the crown of his head. (6) Whatever my parents saw or heard or felt that night, they both understood that something wonderful had happened. 1. 次の英語を日本語に直しなさい。 (1) major in~ で専攻する 地域 ・中 落ち着く (3) neighborhood (5) throughout (7) settle in (9) whatever (8) Neither one of them was able to sleep. Even after she closed her eyes, my mother could see only one thing: my father's face. And (9) my father, who could not stop thinking about her, stayed up all night painting my mother's portrait. たとえ (2) neither (4) happen to~ (6) opposite (8) familiar 何をへとも (10) immediately 2. 下部 (1) (2)について 1947年当時、 母親と父親はどんな人物でしたか。 日本語で答えなさい。 mother 当時20歳でニューヨークの大学に通っていて英語を専攻していた。 本や考えに激情していて、それらを熱心に読んでいつか作家になると 望んでいた。 father 彼は当時売れない作家で、ニューヨークの中学校で 絵を教えることでお金を稼いでいた。 3. 下線部 (3)について、この日の夜に起きたことを要約しなさい。 どちらのもでない 偶然でする 反対の 精通している (7) Like two old friends catching up after a long absence from one another, they talked 6. 下線部 (6) を日本語に訳しなさい。 and talked for hours. At the end of the evening, my mother wrote her telephone number on the inside cover of Great Expectations and gave the book to my father. He said goodbye to her, gently kissing her on the forehead, and they walked off in opposite directions into the night. 4. 下線部 (4) を there の場所を明確にして日本語に訳しなさい。 彼女はミルキーウェイと呼ばれるレストランで使用済みのコピーの ディケンズの小説大いなる遺産を持ってきてどんどん読み進めていた。 5. 下線部 (5)の正しい日本語訳を以下の1~4から選びなさい。 1. ウェイターが来て、 母親にもし父親と相席したいなら それでも良いと返答した。 (2. ウェイターが来て、 母親に他のお客さんと相席してもらえるかどうか尋ねた。 3.ウェイターが通り過ぎて、他のお客さんにテーブルを譲った。 4. ウェイターが来て､ もし他のお客さんと相席をしたいなら、 それでも良いと返答し たとえ私の両親があの夜何を見て、聞いて、感じたとしても お互い何か素敵なことが起こったのだと理解した。 裏面

数A二次関数です。下の式から上の式に、どう計算したらなるのか教えてください。

とする とす Dとす D とす 0 Dと the D 必要 とず + ED グラフがx軸と共有点をもつための必要十分条 件は D≧0であるから 1+16m≥0 188 (1) 2次方程式x2+2mx+m+2=0の判別 式をDとすると D=(2m)²-4.1.(m+2) =4(m²-m-2)=4(m+1Xm-2) グラフがx軸に接するための必要十分条件は D = 0 であるから (m+1)(m-2)=0 よって [1] m=-1のとき 関数は y=x2-2x+1 すなわち y=(x-1)2 よって、 接点の座標は [2] m=2のとき m=-1, 2 [1],[2] から よって 関数は y=x² + 4x+4-0 y=(x+2)2 すなわち よって、 接点の座標は [参考] 2=1 m=-1のとき 接点の座標 (1,0) m=2のとき 接点の座標 (−20) すなわち よって ゆえに [1] m= 1 mz-16 (1, 0) よい｡ [別解 (接点の座標の求め方) 接点のx座標は、 2次方程式 x2+2mx+m+2 = 0 =m²-1(m+2)=m²-m-2としても (-2, 0) C m= x=- の重解であるから よって、 接点の座標は m=-1のとき (1,0), m=2のとき (-2,) (2) 2次方程式x²-√5x+m²+2m=0 の判別式 をDとすると D=(-√5)²-4・1. (m²+2m) =-4m²-8m+5 グラフがx軸に接するための必要十分条件は D=0であるから -4m²-8m+5= 0 5 -2 2m 2.1 4m2+8m-5=0 (2m-1)(2m+5) = 0 =1のとき 関数は y=x²-√√5x+- =-m 5 4 すなわち x = (x - √5)² よって、接点の座標は (12) 2' [2] - のとき すなわち y= x- よって、接点の座標は (①) [1],[2] から y=x²-√5x+² √5 1² m= =1/12/201 接点の座標 (√5.0) 5 =-2のとき接点の座標 (1/25) √√5 2' のとき 別解 (接点の座標の求め方) 接点のx座標は、 2次方程式 x²-√5x+m²+2m = 0 の重解であるから x=- よって、 接点の座標は 145/ m= n=1/1/2の のとき 5 m=- のとき 2 189 (1) グラフとx軸 の共有点のx座標は x2-2x-8=0 の実数 解である｡ 左辺を因数分解すると (x+2)(x-4)= 0 x=- よって x=-2.4 ゆえに, 求める線分の 長さは (2) グラフとx軸の共有 点のx座標は x2+6x+7=0 の実数 解である。 解の公式により -√√5 √√5 2.1 2 -3+√3²-1.7 2 0 -2 0 ty (1=-3+√2 よって 求める線分の長さは -8 -3-v2 -6- -3+√2-(-3-√2)=2√2 09 4 0=8. 4-(-2)=6S set y=x2+6x+7 ber y=x2-2x-8 2√/2... x -3+√2 ty 0x 190 2次方程式x2-4x+2m=0の判別式をDと すると である。 よって, グラフ m<2のと m=2のと m>2のと D 4 [参考 D=(-4) ² D> 0 となる D = 0 とな D<0 とな 別解 = (−2) ■■■指 グラフの頂 関数の式を変 このグラフは, である。 よって, グラ 2m-4> 2m-4= 02m-44 * 2m-4>0 Ny 197 191 (1) x軸 (-2, 0) 10 と表される この放物線 -4=c ゆえに, 1 y=-2 (2) x軸と点 は この放物 12= ゆえに,