1.C
\(sinx+2=0\Rightarrow sinx=-2< -1\) vô nghiệm
2.D
\(tan5x=-\dfrac{9}{5}\) phương trình \(tanu=a\) luôn luôn có nghiệm
3B
\(y=cosx-cos\left(x-\dfrac{2\pi}{3}\right)+3=-2sin\left(x-\dfrac{\pi}{3}\right).sin\left(\dfrac{\pi}{3}\right)+3\)
\(=-\sqrt{3}sin\left(x-\dfrac{\pi}{3}\right)+3\ge3-\sqrt{3}\)
4D
\(cos3x=-\dfrac{\sqrt{3}}{2}\Leftrightarrow3x=\pm\dfrac{5\pi}{6}+k2\pi\)
\(\Rightarrow x=\pm\dfrac{5\pi}{18}+\dfrac{k2\pi}{3}\) có 3 nghiệm trên khoảng đã cho \(x=\left\{\dfrac{5\pi}{18};\dfrac{7\pi}{18};\dfrac{17\pi}{18}\right\}\)
5.
\(cos\left(5x-1\right)=m^2\)
Do \(-1\le cos\left(5x-1\right)\le1\Rightarrow-1\le m^2\le1\)
\(\Rightarrow m^2\le1\)
\(\Rightarrow-1\le m\le1\)
6.
\(5sinx-m+2=0\Rightarrow sinx=\dfrac{m-2}{5}\)
Do \(-1\le sinx\le1\) nên pt có nghiệm khi:
\(-1\le\dfrac{m-2}{5}\le1\Rightarrow-3\le m\le7\)
7.
\(\left(sin2x-cosx\right)\left(2cosx-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin2x=cosx\\2cosx=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sin2x=sin\left(\dfrac{\pi}{2}-x\right)\\cosx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{\pi}{2}-x+k2\pi\\2x=\dfrac{\pi}{2}+x+k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+\dfrac{k2\pi}{3}\\x=\dfrac{\pi}{2}+k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
