Câu hỏi:

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

Câu 1:

Giải hệ phương trình $\left\{\begin{array}{l}x+y=\frac{2\pi }{3}\\ tanx.tany=3\end{array}\right.$

$\left\{\begin{array}{l}x=\pi +k\pi \\ y=-\frac{\pi }{3}-k\pi \end{array}\right.$

A. $\left\{\begin{array}{l}x=\frac{2\pi }{3}+k\pi \\ y=-k\pi \end{array}\right.$

B. $\left\{\begin{array}{l}x=\frac{\pi }{3}+k\pi \\ y=\frac{\pi }{3}-k\pi \end{array}\right.$

C. $\left\{\begin{array}{l}x=\frac{5\pi }{6}+k\pi \\ y=-\frac{\pi }{6}-k\pi \end{array}\right.$ 

Câu 2:

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 3:

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 4:

Một họ nghiệm của phương trình $\cos 10x-\cos 8x-\cos 6x+1=0.$

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

A. $x=\frac{\mathrm{\pi }}{3}+\frac{k\mathrm{\pi }}{4}$

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

C. $x=\frac{k\mathrm{\pi }}{4}$

Câu 5:

Tìm m để phương trình msinx+5cosx=m+1 có nghiệm

A. $m\le 12$

B. $m\le 6$

C. $m\le 24$

D. $m\le 3$ 

Câu 6:

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