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 cos3x.tan5x=sin7x.

$x=\frac{n\mathrm{\pi }}{2}; x=\frac{\mathrm{\pi }}{20}+\frac{k\mathrm{\pi }}{13}\left(k, n\in Z\right)$

A. $x=\frac{n\mathrm{\pi }}{2}; x=\frac{\mathrm{\pi }}{20}+\frac{k\mathrm{\pi }}{10}\left(k, n\in Z\right)$

B. $x=n\mathrm{\pi }; x=\frac{3\mathrm{\pi }}{5}+\frac{2k\mathrm{\pi }}{7}\left(k, n\in Z\right)$

C. $x=n\mathrm{\pi }; x=\frac{3\mathrm{\pi }}{5}+\frac{7k\mathrm{\pi }}{13}\left(k, n\in Z\right)$ 

Câu 2:

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 3:

Giải phương trình $8\sin x=\frac{\sqrt{3}}{\cos x}+\frac{1}{\sin x}$

$x=-\frac{\mathrm{\pi }}{6}+\frac{k\mathrm{\pi }}{2}; x=\frac{\mathrm{\pi }}{12}+\frac{k\mathrm{\pi }}{2}\left(k\in Z\right)$

A. $x=\frac{\mathrm{\pi }}{12}+\frac{k\mathrm{\pi }}{4}\left(k\in Z\right)$

B. $x=\pm \frac{\mathrm{\pi }}{6}+k\mathrm{\pi }; x=-\frac{\mathrm{\pi }}{12}+\frac{k\mathrm{\pi }}{2}\left(k\in Z\right)$

C. $x=-\frac{\mathrm{\pi }}{6}+k\mathrm{\pi }; x=-\frac{\mathrm{\pi }}{12}+\frac{k\mathrm{\pi }}{2}\left(k\in Z\right)$ 

Câu 4:

Phương trình ${\cos }^{2}x-4\cos x+3=0$ có nghiệm là:

$x=\pi +k2\pi \left(k\in Z\right)$

A. $x=k\pi \left(k\in Z\right)$

B. $x=\pi +k\pi \left(k\in Z\right)$

C. $x=k2\pi \left(k\in Z\right)$ 

Câu 5:

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 6:

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

A. $\left[\begin{array}{l}x=-\frac{\pi }{36}+\frac{k2\pi }{3}\\ x=\frac{5\pi }{36}+\frac{k2\pi }{3}\end{array}\right.(k\in Z)$

B. $\left[\begin{array}{l}x=-\frac{\pi }{36}+\frac{k\pi }{3}\\ x=\frac{5\pi }{36}+\frac{k\pi }{3}\end{array}\right.(k\in Z)$

C. $\left[\begin{array}{l}x=\frac{\pi }{36}+\frac{k2\pi }{3}\\ x=-\frac{5\pi }{36}+\frac{k2\pi }{3}\end{array}\right.(k\in Z)$

D. $\left[\begin{array}{l}x=-\frac{\pi }{36}+k2\pi \\ x=\frac{5\pi }{36}+k2\pi \end{array}\right.(k\in Z)$