Để phương trình: $\displaystyle {{\sin }^{2}}x+2\left( m+1 \right)\sin x-3m\left( m-2 \right)=0$ có nghiệm, các giá trị thích hợp của tham số$\displaystyle m$ là
A. $\displaystyle \left[ \begin{array}{l}-\frac{1}{2}\le m<\frac{1}{2}\\1\le m\le 2\end{array} \right.$ 
B. $\displaystyle \left[ \begin{array}{l}-\frac{1}{3}\le m\le \frac{1}{3}\\1\le m\le 3\end{array} \right.$ 
C. $\displaystyle \left[ \begin{array}{l}-2\le m\le -1\\0\le m\le 1\end{array} \right.$ 
D. $\displaystyle \left[ \begin{array}{l}-1\le m\le 1\\3\le m\le 4\end{array} \right.$

Phương trình $\displaystyle \sin 8x-\cos 6x=\sqrt{3}\left( \sin 6x+\cos 8x \right)$ có các họ nghiệm là
A. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{4}+k\pi \\x=\frac{\pi }{12}+k\frac{\pi }{7}\end{array} \right.$ 
B. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{3}+k\pi \\x=\frac{\pi }{6}+k\frac{\pi }{2}\end{array} \right.$ 
C. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{5}+k\pi \\x=\frac{\pi }{7}+k\frac{\pi }{2}\end{array} \right.$ 
D. $\displaystyle \left[ \begin{array}{l}x=\frac{\pi }{8}+k\pi \\x=\frac{\pi }{9}+k\frac{\pi }{3}\end{array} \right.$

Tập xác định của hàm số $y=\frac{2}{{\cos x-\cos 3x}}$ là
A. $\mathbb{R}\backslash \left\{ {k2\pi ,k\in \mathbb{Z}} \right\}$ 
B. $\mathbb{R}\backslash \left\{ {k\frac{\pi }{2},k\in \mathbb{Z}} \right\}$ 
C. $\mathbb{R}\backslash \left\{ {k\frac{\pi }{4},k\in \mathbb{Z}} \right\}$ 
D. $\mathbb{R}\backslash \left\{ {k\pi ,k\in \mathbb{Z}} \right\}$

Cho hàm số $y=\sqrt{2-\sin x}.$ Tập xác định của hàm số là
A. $\left( -\infty ;\sqrt{2} \right].$
B. $\left[ -\sqrt{2};\sqrt{2} \right].$
C. $R.$
D. $\left[ \sqrt{2};+\infty \right).$

Hàm số $y=\sqrt{\frac{1-\sin x}{1+\sin x}}$ xác định khi
A. $\forall x\in R.$
B. $\forall x\in \left\{ R\backslash -\frac{\pi }{2}+k2\pi |k\in Z \right\}.$
C. $x
e \frac{\pi }{2}+k2\pi ,k\in Z.$
D. $x
e \pm \frac{\pi }{2}+k2\pi ,k\in Z.$

Phương trình $\displaystyle {{\sin }^{2}}2x-2{{\cos }^{2}}x+\frac{3}{4}=0$ có nghiệm là
A. $\displaystyle x=\pm \frac{\pi }{6}+k\pi $ 
B. $\displaystyle x=\pm \frac{\pi }{4}+k\pi $ 
C. $\displaystyle x=\pm \frac{\pi }{3}+k\pi $ 
D. $\displaystyle x=\pm \frac{2\pi }{3}+k\pi $

Cho phương trình: $\displaystyle \frac{{{\sin }^{6}}x+{{\cos }^{6}}x}{{{\cos }^{2}}x-{{\sin }^{2}}x}=2m.\tan 2x$, trong đó m là tham số. Để phương trình có nghiệm, các giá trị thích hợp của m là
A.  $\displaystyle m<-\frac{1}{8}\ hay\ m>\frac{1}{8}$ .
B.  $\displaystyle m\le -\frac{1}{4}\ hay\ m\ge \frac{1}{4}$. 
C. $\displaystyle m\le -\frac{1}{2}\ hay\ m\ge \frac{1}{2}$. 
D. $\displaystyle m\le -1\ hay\ m\ge 1$.

Choose one sentence that has the same meaning to the root one:
People say that he gets a high salary.
A. It is said that he gets a high salary.
B. It is said for him to gets high salary.
C. He is said that he gets a high salary.
D. That he gets a high salary is said.

Choose one sentence that has the same meaning to the root one:
“If I were you, I would take the job,” said my room-mate.
A. My room-mate was thinking about taking the job.
B. My room-mate advised me to take the job.
C. My room-mate introduced the idea of taking the job to me.
D. My room-mate insisted on taking the job for me.

Choose one sentence that has the same meaning as the root one:
Tim is likely to fail if he takes the exam without studying.
A. Tim will fail if he takes the exam without studying.
B. It’s probable that Tim will fail the exam if he doesn’t study.
C. It’s certain that Tim will pass the exam if he studies.
D. It’s certain that Tim will fail because he doesn’t study.