`~rai~`
\(8)y=\sqrt{\dfrac{\cos{3x}+2}{\cos{x}+1}}\\ĐKXĐ:\begin{cases}\dfrac{\cos{3x}+2}{\cos{x}+1}\ge 0\\\cos{x}\ne -1\end{cases}.(1)\\\text{Ta có:}\\+)-1\le \cos{3x}\le 1\\\Leftrightarrow 1\le\cos{3x}+2\le 3\\\Rightarrow \cos{3x}+2>0\quad\forall x.(2)\\+)-1\le \cos{x}\le 1\\\Leftrightarrow 0\le \cos{x}+1\le 2\\\Rightarrow \cos{x}+1\ge 0\quad\forall x.(3)\\\text{Từ (2) và (3)}\Rightarrow \dfrac{\cos{3x}+2}{\cos{x}+1}>0\quad\forall x\quad nên\\(1)\Leftrightarrow \cos{x}\ne -1\\\Leftrightarrow x\ne \pi+k2\pi.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\{\pi+k\pi|k\in\mathbb{Z}\}.\\9)y=\dfrac{\tan{2x}-1}{\sqrt{1+\sin{x}}+1}\\ĐKXĐ:\begin{cases}\cos{2x}\ne 0\\1+\sin{x}\ge 0.\end{cases}(1)\\\text{Ta có:}-1\le \sin{x}\le 1\\\Leftrightarrow 0\le \sin{x}+1\le 2\\\Rightarrow \sin{x}+1\ge 0\quad\forall x\quad nên\\(1)\Leftrightarrow \cos{2x}\ne 0\\\Leftrightarrow 2x\ne \dfrac{\pi}{2}+k\pi\\\Leftrightarrow x\ne \dfrac{\pi}{4}+k\dfrac{\pi}{2}.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{\dfrac{\pi}{4}+k\dfrac{\pi}{2}\Big|k\in\mathbb{Z}\right\}.\)
