Câu 1c:
$\sin2x-(6m+7)\sin2x=2m$
$\Leftrightarrow (-6m-6)\sin2x=2m$
ĐK: $m\ne -1$
$\Leftrightarrow \sin2x=\dfrac{2m}{-6m-6}$
Để phương trình có nghiệm: $-1\le\dfrac{2m}{-6m-6}\le 1$
$+)\dfrac{2m}{-6m-6}\ge -1$
$\Leftrightarrow \dfrac{2m+(-6m-6)}{-6m-6}\ge 0$
$\Leftrightarrow \dfrac{-4m-6}{-6m-6}\ge 0$
$\Leftrightarrow \dfrac{4m+6}{6m+6}\le 0$
$\Leftrightarrow \dfrac{-3}{2}\le m<-1$
$+) \dfrac{2m}{-6m-6}\le 1$
$\Leftrightarrow \dfrac{2m+6m-6}{-6m-6}\le 0$
$\Leftrightarrow \dfrac{8m-6}{6m+6}\ge 0$
$\Leftrightarrow m<-1; m\ge \dfrac{3}{4}$
Vậy $m\in \Bigg[\dfrac{-3}{2};-1\Bigg)\cup \Bigg(\dfrac{3}{4};+\infty\Bigg)$
Câu 2:
$\sin(x+\dfrac{\pi}{4})=1$
$\Leftrightarrow x+\dfrac{\pi}{4}=\dfrac{\pi}{2}+k2\pi$
$\Leftrightarrow x=\dfrac{\pi}{4}+k2\pi$
$0\le x\le 3\pi\Rightarrow -0,125\le k\le 1,375$
$\Rightarrow k\in\{0;1\}$
$\to$ 2 nghiệm
