Câu hỏi:

Giải phương trình $1+\sin x+\cos 3x=\cos x+\sin 2x+\cos 2x$

$x=k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{6}+\frac{\mathrm{k\pi }}{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{5\mathrm{\pi }}{7}+\mathrm{k\pi }$

A. $x=k2\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{3}+\frac{k2\pi }{3}, \mathrm{x}=\frac{\mathrm{\pi }}{12}+\mathrm{k\pi }, \mathrm{x}=\frac{5\mathrm{\pi }}{12}+\mathrm{k\pi }$

Câu 1:

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

Câu 2:

Phương trình ${\sin }^{2}3x+\left(m^2-3\right)\sin 3x+m^2-4=0$ khi m=1 có nghiệm là:

$x=-\frac{\pi }{6}+k2\pi \left(k\in Z\right)$

A. $x=\frac{\pi }{6}+\frac{k2\pi }{3}\left(k\in Z\right)$

B. $x=-\frac{\pi }{6}+\frac{k2\pi }{3}\left(k\in Z\right)$

C. $x=\pm \frac{\pi }{6}+\frac{k2\pi }{3}\left(k\in Z\right)$ 

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:

Giải phương trình $1+\cos x+\cos 2x+\cos 3x=0.$

$x=\pm \frac{\mathrm{\pi }}{2}+2k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}$

A. $x=\frac{\mathrm{\pi }}{2}+2k\mathrm{\pi }, \mathrm{x}=\pm \frac{\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}$

B. $x=\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{3}+\frac{\mathrm{k}2\mathrm{\pi }}{3}$

C. $x=-\frac{\mathrm{\pi }}{2}+k\mathrm{\pi }, \mathrm{x}=\frac{\mathrm{\pi }}{6}+\frac{\mathrm{k}2\mathrm{\pi }}{3}$ 

Câu 6:

Giải phương trình $\cos x.\cos \frac{x}{2}. \cos \frac{3x}{2}-\sin x.\sin \frac{x}{2}.\sin \frac{3x}{2}=\frac{1}{2}$

A. $x=-\frac{\mathrm{\pi }}{4}+k\mathrm{\pi }; \mathrm{x}=\frac{\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=\frac{5\mathrm{\pi }}{6}+\mathrm{k}2\mathrm{\pi }; \mathrm{x}=-\frac{\mathrm{\pi }}{2}+\mathrm{k}2\mathrm{\pi }\left(\mathrm{k}\in \mathrm{Z}\right)$