微分の問題なのですが、 最後の式変形が分かりません💦 教えてください!!

(10) )y=cos4x ダ-2c054x.(c05枚). 20054が(-5lnt) .4ス) =8c0stX Sintx

（1）についてです。 どうしてcos2x＝1になるんですか?

-0 X 文0 sin4x 次の極限値を求めよ。 教 p.124 問 15 tan2x (2)* lim 1- cos2x ズ→0 X

vivid2 lesson4のPart4です！英語が得意な方訳をお願いしたいです！よろしくお願いします🙇‍♀️ Some people feel it pleasant to have lucky numbers, such as 7, 8 or 15. They try... Read More

form xvii can be changed into the Latin sentence Some people feel it pleasant to have lucky numbers, such as 7, 8 or 15. They try to avoid numbers associated with unlucky things. In Christian countries, many people feel uncomfortable when their hotel room is on the 13th floor. The number 13 has traditionally been G considered unlucky. This might be because there were thirteen people at the Last Supper before Jesus was betrayed. So hotels in Christian countries often refer to their 13th floor as the 14th one. In Italy, the unlucky number is 17. Its numera form xvii can be changed into the Latin sentence Thus, vixi, which implies that “my life is over. being careful about number associations is importa" for better understanding between a cultures.

vivid2 lesson4のPart3です！英語が得意な方訳をお願いしたいです！よろしくお願いします🙇‍♀️ People in other countries are also careful about People in China feel it lucky t... Read More

People in other countries are also careful about numbers. People in China feel it lucky that they can have a car with the number 8 on the 1license plate. The pronunciation of 8 in their language is easily associated with a word meaning “prosperity 5 or fortune.” European countries have their own number associations. The number 7 is widely considered lucky. Some Europeans have long felt a G sense of completion in the number 7, as in the Seven 0 Heavens and the Seven Wise Men. In Germany, the number 4 is another lucky number. People in Norway regard the number 9 as lucky, and people in Spain believe the number 15 15 is lucky. In short, different numbers have different " cultural associations.

vivid2 lesson4のPart2です！英語が得意な方訳をお願いしたいです！よろしくお願いします🙇‍♀️ Numbers in Japanese often have the same sounds as other words. The number 4 can ... Read More

Numbers in Japanese often have the same sounds as other words. The number 4 can stand for “shi," which refers to death. And the number9 can sound G like “ku," which means suffering. These numbers sound uncomfortable for people in Japan. Japanese people sometimes throw five-yen coins into offering boxes at shrines. Five yen in Japanese sounds like “go-en.” They wish that their five-yen coins will bring good fortune. As the examples above show, native Japanese speakers are careful M 10 about how numbers are pronounced in the language. Japanese numbers have another side. 5963, or “go-ku-ro-san," can mean: “Thank you for your hard work.” 530, or “go-mi-zero,” can refer to zero waste.

vivid2 lesson4のPart1です。 次のテスト範囲なのですが、英語が得意な方訳をお願いしたいです！よろしくお願いします🙇‍♀️ What will the combination of two letters and a number in2 mean? Th... Read More

What will the combination of two letters and a number in2 mean? The number 2 has the same sound as “to.” Then, in2 is read as “into.” What about d8? The number 8 sounds like “ate,” so d8 is read as date." 5 Wordplay like d8 can be found in casual emails between friends. How can you read the following two sentences? G2g. CU 18r. You can read G as “go." Cand U will sound like “see” and “you," respectively. Then, the sentences will mean: “Got " 10 to go. See you later." The wordplay above is available because numbers Sometimes have the same pronunciations that other G words have. Can you create new words from unique combinations? 15

波線を引いたところが 計算をしたのですが、答えまでたどり着けません💦 教えてください!!

1 1 と変形できることを利用して, 1 ロ練習61 ーロ 4k?-1 |k+1 1 となる。また, 1 1 1 である。 1 n 3 15 35 1023 4k?-1 nさ

赤線の式から青線の式になる理由を教えてください。

tan15°= tan(45°-30°) tan45°-tan30° 1+ tan45°tan30° V3 1 V3 <3-1 V3+1 tan75°= tan(45°+30°) (V3-1)2 (V3 + 1)(V3 -1) 1-2/3 _2-J3 =2-V3 2 ニ 1 1+ V3 tan45°+tan30° 1-tan45°tan30° 1 1-1. V3 V3+1 V3-1 って, 求める直線の方程式は (V3+1)? 4+2、3 =2+V3 2 三 y=(2-V3)x, y=(2+/3)x

数Ⅲ 積分 (3)の式変形がわかりません。どこから8xと2xが出てくるのでしょうか？教えてください。

X=xp(xso: -1 Sin X +Oし (3)|cos3xsin 5xdx=→\ (sin 8x +sin2x)dx (sin 8x +sin 2x)dx 1 cos8.x 16 Gcos2.x +C (4) sin2xsin4xdx=-→(cos6.x-cos2x)dx 1 sin6x+-sin 2x +C cl 1 (5) |cosdx=1+ cosx)dx Joog-tcmda 2北 COS 1 ラメ+-sinx+C 2

数学の質問です。範囲は三角関数の周期関数です。 写真の部分について質問です。 なぜ、周期のkに絶対値をつけるのでしょうか…？「y＝sinkθ の周期は 2π/｜k｜」になるんですか？ というのも、周期関数の定義は、「0でない定数pがあり、f(x＋p)＝f(x) がどん... Read More

<三角関数の周期> sin(0+2x)=sin0, cos(0+2x)=cos0 であるから, y=sin0. y=cosθの周期は 2元であ る。また, tan(0+x)=tan0 であるから, y=tan0の周期は元である。 f(x)=sinkx (kは定数) とすると A*)-sind(**)- 2元 2元 =sin(kx+2x)=sinkx=f(x) 2元 関数 y=sink0の周期は ソ=sin40 の周 よって 例 2元 期は ー 2 π 4 2元 関数 y=cos k0 の周期は Tel" 同様に y=cos 30 の周期は 2 3てであるから, T 関数 y=tan k0 の周期は ソ=cos(30-a) の周期 また,周期がp(カ>0) の関数f(x) に対し, 関数 f(x+a) (aは定数, aキ0)の周期もかである。 もそえ -元である。