`~rai~`
\(3.y=\dfrac{3\cos{4x}-3}{\sqrt{2-2\cos{x}}-2}\\ĐKXĐ:\begin{cases}2-2\cos{x}\ge 0\\\sqrt{2-2\cos{x}}\ne 2\end{cases}.(1)\\\text{Ta có:}-1\le\cos{x}\le 1\\\Leftrightarrow 1\ge -\cos{x}\ge -1\\\Leftrightarrow 3\ge 2-\cos{x}\ge 1\\\Rightarrow 2-2\cos{x}>0\quad\forall x\quad nên\\(1)\Leftrightarrow \sqrt{2-2\cos{x}}\ne 2\\\Leftrightarrow 2-2\cos{x}\ne 4\\\Leftrightarrow \cos{x}\ne -1\\\Leftrightarrow x\ne \pi+k2\pi.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{\pi+k2\pi|k\in\mathbb{Z}\right\}.\\4.y=\dfrac{1-\cot{3x}}{1-\sqrt{1+\sin{3x}}}\\ĐKXĐ:\begin{cases}\sin{3x}\ne 0\\1+\sin{3x}\ge 0\\\sqrt{1+\sin{3x}}\ne 1\\\end{cases}(1)\\\text{Ta có:}-1\le \sin{3x}\le 1\\\Leftrightarrow 0\le 1+\sin{3x}\le 2\\\Rightarrow 1+\sin{3x}\ge 0\quad\forall x\quad nên\\(1)\Leftrightarrow \begin{cases}\sin{3x}\ne 0\\\sqrt{1+\sin{3x}}\ne 1\end{cases}\\\Leftrightarrow \begin{cases}\sin{3x}\ne 0\\1+\sin{3x}\ne 1\end{cases} \\\Leftrightarrow \sin{3x}\ne 0\\\Leftrightarrow 3x\ne k\pi\\\Leftrightarrow x\ne k\dfrac{\pi}{3}.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{k\dfrac{\pi}{3}\Big|k\in\mathbb{Z}\right\}.\\5.y=\cot{2x}+\cot{x}\\ĐKXĐ:\begin{cases}\sin{2x}\ne 0\\\sin{x}\ne 0\end{cases}\\\Leftrightarrow \begin{cases}x\ne k\pi\\2x\ne k\pi\end{cases}\\\Leftrightarrow \begin{cases}x\ne k\pi\\x\ne k\dfrac{\pi}{2}\end{cases}\\\Leftrightarrow x\ne k\dfrac{\pi}{2}.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{k\dfrac{\pi}{2}\Big|k\in\mathbb{Z}\right\}.\)
