a.

Đặt \(sinx+cosx=t\in\left[-\sqrt{2};\sqrt{2}\right]\)

\(\Rightarrow1+2sinx.cosx=t^2\Rightarrow2sinx.cosx=t^2-1\)

Phương trình trở thành:

\(3t=2\left(t^2-1\right)\)

\(\Leftrightarrow2t^2-3t-2=0\)

\(\Rightarrow\left[{}\begin{matrix}t=2>\sqrt{2}\left(loại\right)\\t=-\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow sinx+cosx=-\dfrac{1}{2}\)

\(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=-\dfrac{1}{2}\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=-\dfrac{\sqrt{2}}{8}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{4}=arcsin\left(-\dfrac{\sqrt{2}}{8}\right)+k2\pi\\x+\dfrac{\pi}{4}=\pi-arcsin\left(-\dfrac{\sqrt{2}}{8}\right)+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+arcsin\left(-\dfrac{\sqrt{2}}{8}\right)+k2\pi\\x=\dfrac{3\pi}{4}-arcsin\left(-\dfrac{\sqrt{2}}{8}\right)+k2\pi\end{matrix}\right.\)

b.

ĐKXĐ: \(x\ne\dfrac{\pi}{2}+k\pi\)

\(1+\dfrac{sinx}{cosx}=2\sqrt{2}sinx\)

\(\Rightarrow sinx+cosx=2\sqrt{2}sinx.cosx\)

\(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=\sqrt{2}sin2x\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=sin2x\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=x+\dfrac{\pi}{4}+k2\pi\\2x=\dfrac{3\pi}{4}-x+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{4}+k2\pi\\x=\dfrac{\pi}{4}+\dfrac{k2\pi}{3}\end{matrix}\right.\)

\(\Leftrightarrow x=\dfrac{\pi}{4}+\dfrac{k2\pi}{3}\)

c.

\(\Leftrightarrow1+sinx+cosx+sinx.cosx=2\)

\(\Leftrightarrow sinx+cosx+sinx.cosx=1\)

Đặt \(sinx+cosx=t\in\left[-\sqrt[]{2};\sqrt{2}\right]\)

\(\Rightarrow sinx.cosx=\dfrac{t^2-1}{2}\)

Phương trình trở thành:

\(t+\dfrac{t^2-1}{2}=1\)

\(\Leftrightarrow t^2+2t-3=0\Rightarrow\left[{}\begin{matrix}t=1\\t=-3\left(loại\right)\end{matrix}\right.\)

\(\Rightarrow sinx+cosx=1\)

\(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=1\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow...\)

a.

\(0< x< \dfrac{\pi}{2}\Rightarrow cosx>0\Rightarrow cosx=\sqrt{1-sin^2x}=\dfrac{\sqrt{6}}{3}\)

\(cos\left(x+\dfrac{\pi}{3}\right)=cosx.cos\left(\dfrac{\pi}{3}\right)-sinx.sin\left(\dfrac{\pi}{3}\right)=\dfrac{\sqrt{6}-3}{6}\)

b.

\(\pi< x< \dfrac{3\pi}{2}\Rightarrow sinx< 0\)

\(\Rightarrow sinx=-\sqrt{1-cos^2x}=-\dfrac{5}{13}\)

\(B=sin\left(\dfrac{\pi}{3}-x\right)=sin\left(\dfrac{\pi}{3}\right).cosx-cos\left(\dfrac{\pi}{3}\right).sinx=...\) (bạn tự thay số bấm máy)

c.

\(A=cos^2x+cos^2y+2cosx.cosy+sin^2x+sin^2y+2sinx.siny\)

\(=\left(cos^2x+sin^2x\right)+\left(cos^2y+sin^2y\right)+2\left(cosx.cosy+sinx.siny\right)\)

\(=1+1+2cos\left(x-y\right)\)

\(=2+2cos\left(\dfrac{\pi}{3}\right)=...\)

d.

\(B=cos^2x+sin^2y+2cosx.siny+cos^2y+sin^2x-2sinx.cosy\)

\(=\left(cos^2x+sin^2x\right)+\left(cos^2y+sin^2y\right)-2\left(sinx.cosy-cosx.siny\right)\)

\(=2-2sin\left(x-y\right)=2-2sin\left(\dfrac{\pi}{3}\right)=...\)

a.

\(90^0< a< 180^0\Rightarrow cosa< 0\)

\(\Rightarrow cosa=-\sqrt{1-sin^2a}=-\dfrac{2\sqrt{2}}{3}\)

\(tana=\dfrac{sina}{cosa}=-\dfrac{\sqrt{2}}{4}\)

b.

\(0< a< 90^0\Rightarrow cosa>0\)

\(\Rightarrow cosa=\sqrt{1-sin^2a}=\dfrac{4}{5}\)

\(tana=\dfrac{sina}{cosa}=\dfrac{3}{4}\)

\(cota=\dfrac{1}{tana}=\dfrac{4}{3}\)

c.

\(A=\dfrac{\dfrac{sina}{cosa}+\dfrac{3cosa}{sina}}{\dfrac{sina}{cosa}+\dfrac{cosa}{sina}}=\dfrac{sin^2a+3cos^2a}{sin^2a+cos^2a}=1+2cos^2a=\dfrac{17}{8}\)

d.

\(A=\dfrac{\dfrac{cosa}{sina}+\dfrac{3sina}{cosa}}{\dfrac{2cosa}{sina}+\dfrac{sina}{cosa}}=\dfrac{cos^2a+3sin^2a}{2cos^2a+sin^2a}=\dfrac{cos^2a+3\left(1-cos^2a\right)}{2cos^2a+\left(1-cos^2a\right)}\)

\(=\dfrac{3-2cos^2a}{1+cos^2a}=\dfrac{19}{13}\)

e.

\(B=\dfrac{\dfrac{3cosa}{sina}+\dfrac{2sina}{cosa}}{\dfrac{sina}{cosa}+\dfrac{cosa}{sina}}=\dfrac{3cos^2a+2sin^2a}{sin^2a+cos^2a}=3\left(1-sin^2a\right)+2sin^2a\)

\(=3-sin^2a=\dfrac{26}{9}\)

f.

\(C=\dfrac{\dfrac{2sina}{cosa}+\dfrac{3cosa}{cosa}}{\dfrac{sina}{cosa}+\dfrac{cosa}{cosa}}=\dfrac{2tana+3}{tana+1}=\dfrac{7}{3}\)

g.

\(C=\dfrac{\dfrac{3sina}{sina}-\dfrac{4cosa}{sina}}{\dfrac{cosa}{sina}-\dfrac{2sina}{sina}}=\dfrac{3-4cota}{cota-2}=1+\sqrt{5}\)

Chọn B

23.

Gọi I là trung điểm MN \(\Rightarrow I\left(3;3\right)\)

\(\Rightarrow\overrightarrow{IN}=\left(2;-1\right)\Rightarrow IN=\sqrt{5}\)

Phương trình đường tròn đường kính MN, nhận I là tâm và có bán kính \(R=IN\) là:

\(\left(x-3\right)^2+\left(y-3\right)^2=5\)

Thay tọa độ E vào pt ta được:

\(\left(x-3\right)^2+4=5\Rightarrow\left(x-3\right)^2=1\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)  \(\Rightarrow x_1x_2=8\)

Cả 4 đáp án của câu này đều sai

24.

Gọi \(M\left(x;y\right)\) là 1 điểm bất kì thuộc \(\Delta\)

Do \(\Delta\) là đường phân giác của góc tạo bởi d và k nên:

\(d\left(M;d\right)=d\left(M;k\right)\Leftrightarrow\dfrac{\left|2x+y\right|}{\sqrt{2^2+1^2}}=\dfrac{\left|x+2y-3\right|}{\sqrt{1^2+2^2}}\)

\(\Leftrightarrow\left|2x+y\right|=\left|x+2y-3\right|\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+y=x+2y-3\\2x+y=-x-2y+3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-y+3=0\\x+y-1=0\end{matrix}\right.\)

- Với \(x-y+3=0\), ta có: 

\(\left(x_E-y_E+3\right)\left(x_F-y_F+3\right)=2.1=2>0\Rightarrow E;F\) nằm cùng phía so với \(x-y+3=0\) (thỏa mãn)

- Với \(x+y-1=0\) ta có:

\(\left(x_E+y_E-1\right)\left(x_F+y_F-1\right)=2.7=14>0\Rightarrow E;F\) nằm cùng phía so với \(x+y-1=0\) (thỏa mãn)

Vậy cả đáp án A và D đều đúng

Tương tự như câu 23, câu 24 đề bài tiếp tục sai

1 Jill reminded John to do the washing up

2 The police ordered his men to search all the shops on that street

3 She blamed me for ignoring the notice about life-saving equipment

4 My aunt advised me not to argut with my father

5 Stella congratulated Jeff on having got an promotion at last

6 Kevin apoligized to Sarah for making her angry

7 The man warn his son to put down the gun

8 Ron denied being in the town on the night of the robbery

9 Ted promise to pay back the money at the end of that month

10 George encouraged Susan to send her story to the magazine

11 Natalie accused Tom of lying to her

Gọi \(M\left(x;y\right)\) là 1 điểm bất kì trên (E) \(\Rightarrow\dfrac{x^2}{16}+\dfrac{y^2}{9}=1\) (1)

Gọi \(M'\left(x';y'\right)\) là ảnh của M qua phép tịnh tiến \(\overrightarrow{v}\Rightarrow M'\in\left(E'\right)\) với (E') là ảnh của (E) qua phép tịnh tiến nói trên

\(\left\{{}\begin{matrix}x'=x+3\\y'=y-2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=x'-3\\y=y'+2\end{matrix}\right.\)

Thế vào (1):

\(\dfrac{\left(x'-3\right)^2}{16}+\dfrac{\left(y'+2\right)^2}{9}=1\)

Hay pt (E') có dạng: \(\dfrac{\left(x-3\right)^2}{16}+\dfrac{\left(y+2\right)^2}{9}=1\)

D C D B C C C D A 

Sam puts up the decorations.

Five guests came to the party.

Molly and Sam play video games with their cousins

The family was celebrating too early. Dad's birthday was two months away.

relationship

celebration

married

golden

quietly

celebratory

refer

1. he dislike being called " the liar " => He dislike people..CALLING HIM THE LIAR.

2. The police are following the suspects => The suspects ..ARE BEING FOLLOWED BY THE POLICE.

3. She always expects to be admired by everybody => She always expects everybody..TO ADMIRE HER...

4. Someone stole his car two days ago => He had ..HIS CAR STOLEN BY SOMEONE TWO DAYS AGO..