Câu hỏi:

Giải phương trình $(\sin x+\sqrt{3}\cos x).\sin 3x = 2$

A. Vô nghiệm

B. $x=\frac{2\mathrm{\pi }}{3}+k\mathrm{\pi }\left(k\in Z\right)$

C. $x=\frac{\mathrm{k\pi }}{12}; x=\frac{2\mathrm{\pi }}{3}+k\mathrm{\pi }\left(k\in Z\right)$ 

Câu 1:

Nghiệm của phương trình $\sin 2x-\sqrt{3}\sin x=0$ là

A. $\left[\begin{array}{l}x=k\pi \\ x=\pm \frac{\pi }{6}+k2\pi \end{array}\right.$

B. $\left[\begin{array}{l}x=k\pi \\ x=\pm \frac{\pi }{6}+k\pi \end{array}\right.$

C. $\left[\begin{array}{l}x=k2\pi .\\ x=\pm \frac{\pi }{3}+k2\pi \end{array}\right.$

D. $x=\pm \frac{\pi }{6}+k2\pi$ 

Câu 2:

Giải phương trình $3{\sin }^{2}2x-\sin 2x\cos 2x-4{\cos }^{2}2x=2$ ta được

A. $x=\frac{1}{2}\arctan 3+\frac{k\pi }{2},x=\frac{1}{2}\arctan \left(-2\right)+\frac{k\pi }{2}\left(k\in Z\right)$

B. $x=\arctan \frac{1+\sqrt{73}}{12}+\frac{k\pi }{2},x=\arctan \frac{1-\sqrt{73}}{12}+\frac{k\pi }{2}\left(k\in Z\right)$

C. $x=\frac{1}{2}\arctan \frac{1+\sqrt{73}}{6}+\frac{k\pi }{2},x=\frac{1}{2}\arctan \frac{1-\sqrt{73}}{6}+\frac{k\pi }{2}\left(k\in Z\right)$

D. $x=\arctan \frac{3}{2}+\frac{k\pi }{2},x=\arctan \left(-1\right)+\frac{k\pi }{2}\left(k\in Z\right)$

Câu 3:

Giải phương trình $2si{n}^{2}2x+sin7x-1=sinx$

$x=-\frac{\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{3}; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{9}$

A. $x=\pm \frac{\mathrm{\pi }}{18}+k2\mathrm{\pi }; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}$

B. $x=\frac{\mathrm{\pi }}{8}+\frac{k\mathrm{\pi }}{4}; x=\frac{\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}; x=\frac{5\mathrm{\pi }}{18}+\frac{k2\mathrm{\pi }}{3}$

C. $x=\frac{\mathrm{\pi }}{8}+\frac{k\mathrm{\pi }}{4}; x=\frac{\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{18}; x=-\frac{5\mathrm{\pi }}{18}+\frac{k\mathrm{\pi }}{3}$

Câu 4:

Giải phương trình $\sin 3x - \frac{2}{\sqrt{3}{\sin }^{2}x}=2\sin x.\cos 2x$

$x=\pm \frac{\mathrm{\pi }}{3}+k2\mathrm{\pi }; \mathrm{x}=\frac{2\mathrm{\pi }}{3}+\mathrm{k}2\mathrm{\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

A. $x=\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }; \mathrm{x}=\frac{\mathrm{\pi }}{6}+\mathrm{k\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

B. $x=\frac{\mathrm{\pi }}{2}+k2\mathrm{\pi }; \mathrm{x}=\frac{\mathrm{\pi }}{3}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=\frac{2\mathrm{\pi }}{3}+\mathrm{k}2\mathrm{\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$

C. Đáp án khác

Câu 5:

Phương trình $\sqrt{3}\sin 2x-\cos 2x+1=0$ có nghiệm là

$\left[\begin{array}{l}x=k\pi \\ x=\frac{\pi }{3}+k\pi \end{array}\right.(k\in Z)$

A. $\left[\begin{array}{l}x=k\pi \\ x=\frac{2\pi }{3}+k2\pi \end{array}\right.(k\in Z)$

B. $\left[\begin{array}{l}x=k2\pi \\ x=\frac{2\pi }{3}+k2\pi \end{array}\right.(k\in Z)$

C. $\left[\begin{array}{l}x=k\pi \\ x=\frac{2\pi }{3}+k\pi \end{array}\right.(k\in Z)$ 

Câu 6:

Giải phương trình cosx+cos3x+2cos5x=0

$x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{5}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{5}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$

A. $\mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$

B. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{15}}{7}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{15}}{7}+\mathrm{k\pi }$

C. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1+\sqrt{17}}{8}+\mathrm{k\pi }, \mathrm{x}=\pm \frac{1}{2}\arccos \frac{1-\sqrt{17}}{8}+\mathrm{k\pi }$