1) Đk: $\sin 2\ne0\Leftrightarrow 2x\ne k\pi$
$\Leftrightarrow x\ne k\dfrac{\pi}{2},(k\in\mathbb Z)$
D
2) Đk: $\sin\left({x-\dfrac{\pi}{3}}\right)$
$\Leftrightarrow x-\dfrac{\pi}{3}\ne k\pi$
$\Leftrightarrow x\ne\dfrac{\pi}{3}+k\pi,(k\in\mathbb Z)$
D
3) $\sin x=3-2m$
$\Rightarrow -1\le3-2m\le1$
$\Rightarrow 1\le m\le2$
A
4) B
5) $\left[ \begin{array}{l} x=\dfrac{\pi}{6}+k2\pi \\ x=\pi-\dfrac{\pi}{6}+k2\pi\end{array} \right .\Leftrightarrow \left[\begin{array}{l} x=\dfrac{\pi}{6}+k2\pi \\ x=\dfrac{5\pi}{6}+k2\pi\end{array} \right .(k\in\mathbb Z)$
A
6) $\cos (2x-30^o)=\dfrac{-\sqrt3}{2}$
$\Rightarrow 2x-30^o=\pm150^o+k360^o$
$\Rightarrow \left[\begin{array}{l} x=90+k180^o\\ x=-60^o+k180^o\end{array} \right .(k\in\mathbb Z)$
A
7) $2x=\dfrac{\pi}{4}+k\pi$
$\Rightarrow x=\dfrac{\pi}{8}+k\dfrac{\pi}{2}$
C
8) $2x=k\pi$
$\Rightarrow x=k\dfrac{\pi}{2}$
$\Rightarrow 0\le k\dfrac{\pi}{2}\le2\pi$
$\Rightarrow 0\le k\le 4$
$\Rightarrow k=0;1;2;3;4\Rightarrow x=0;\dfrac{\pi}{2}$
5 nghiệm
A
9) $\Rightarrow 1-{\cos}^2x-\cos x-1=0$
$\Rightarrow {\cos }^2x+\cos x=0$
$\Rightarrow \cos x(\cos x+1)=0$
$\Rightarrow \left[ \begin{array}{l} \cos x=0 \\ \cos x=-1\end{array} \right .\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{2}+k\pi \\ x=\pi+k2\pi\end{array} \right .$
A
