Câu 30: \(cos\left(3x-\frac{\pi}{4}\right)+4=2m\)
=>\(cos\left(3x-\frac{\pi}{4}\right)=2m-4\)
Để phương trình vô nghiệm thì \(\left[\begin{array}{l}2m-4<-1\\ 2m-4>1\end{array}\right.\Rightarrow\left[\begin{array}{l}2m<3\\ 2m>5\end{array}\right.=>\left[\begin{array}{l}m<\frac32\\ m>\frac52\end{array}\right.\)
=>Chọn A
Câu 29: \(\sin\left(2x+\frac{\pi}{3}\right)=cos2x\)
=>\(\sin\left(2x+\frac{\pi}{3}\right)=\sin\left(\frac{\pi}{2}-2x\right)\)
=>\(\left[\begin{array}{l}2x+\frac{\pi}{3}=\frac{\pi}{2}-2x+k2\pi\\ 2x+\frac{\pi}{3}=\pi-\frac{\pi}{2}+2x+k2\pi\end{array}\right.\Rightarrow\left[\begin{array}{l}4x=\frac{\pi}{2}-\frac{\pi}{3}+k2\pi=\frac{\pi}{6}+k2\pi\\ 0x=\frac16\pi+k2\pi\left(vôlý\right)\end{array}\right.\)
=>\(x=\frac{\pi}{24}+\frac{k\pi}{2}\)
=>Chọn A
Câu 28: Đặt y=1/2
=>sin x=1/2
=>\(\left[\begin{array}{l}x=\frac{\pi}{6}+k2\pi\\ x=\pi-\frac{\pi}{6}+k2\pi=\frac56\pi+k2\pi\end{array}\right.\)
\(x\in\left\lbrack-\frac32\pi;2\pi\right\rbrack\)
=>\(\left[\begin{array}{l}\frac{\pi}{6}+k2\pi\in\left\lbrack-\frac32\pi;2\pi\right\rbrack\\ \frac56\pi+k2\pi\in\left\lbrack-\frac32\pi;2\pi\right\rbrack\end{array}\right.\Rightarrow\left[\begin{array}{l}2k+\frac16\in\left\lbrack-\frac32;2\right\rbrack\\ 2k+\frac56\in\left\lbrack-\frac32;2\right\rbrack\end{array}\right.\)
=>\(\left[\begin{array}{l}2k\in\left\lbrack-\frac{10}{6};\frac{11}{6}\right\rbrack\\ 2k\in\left\lbrack-\frac{14}{6};\frac76\right\rbrack\end{array}\right.\Rightarrow\left[\begin{array}{l}k\in\left\lbrack-\frac56;\frac{11}{12}\right\rbrack\\ k\in\left\lbrack-\frac76;\frac{7}{12}\right\rbrack\end{array}\right.\Rightarrow\left[\begin{array}{l}k\in\left\lbrace0\right\rbrace\\ k\in\left\lbrace-1;0\right\rbrace\end{array}\right.\)
=>Chọn B
