`~rai~`
\(a)y=\dfrac{\sqrt{4-\sin2x}}{\cos x}\\ĐKXĐ:\begin{cases}4-\sin2x\ge 0\\\cos x\ne 0\end{cases}\\\Leftrightarrow \begin{cases}\sin2x\le 4\text{(luôn đúng vì }-1\le \sin2x\le 1)\\x\ne\dfrac{\pi}{2}+k\pi(k\in\mathbb{Z})\end{cases}\\TXĐ:D=\mathbb{R}\backslash\left\{\dfrac{\pi}{2}+k\pi\Big|k\in\mathbb{Z}\right\}.\\b)\dfrac{6\tan x}{\sin x+1}\\ĐKXĐ:\begin{cases}\cos x\ne 0\\\sin x\ne 1\end{cases}\\\Leftrightarrow \begin{cases}x\ne\dfrac{\pi}{2}+k\pi\\x\ne-\dfrac{\pi}{2}+k2\pi\end{cases}\\\Leftrightarrow x\ne\dfrac{\pi}{2}+k\pi.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{\dfrac{\pi}{2}+k\pi\Big|k\in\mathbb{Z}\right\}.\\c)\dfrac{5}{\tan x}-\cot2x\\ĐKXĐ:\begin{cases}\cos x\ne 0\\\tan x\ne 0\\\sin 2x\ne 0\end{cases}\\\Leftrightarrow \begin{cases}x\ne \dfrac{\pi}{2}+k\pi\\x\ne k\pi\\2x\ne k\pi\end{cases}\\\Leftrightarrow \begin{cases}x\ne\dfrac{\pi}{2}+k\pi\\x\ne k\pi\\x\ne k\dfrac{\pi}{2}\end{cases}\\\Leftrightarrow x\ne k\dfrac{\pi}{2}.(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{k\dfrac{\pi}{2}\Big|k\in\mathbb{Z}\right\}\\d)\dfrac{3}{\sin2x-1}+\dfrac{1}{\cos x}\\ĐKXĐ:\begin{cases}\sin2x\ne 1\\\cos x\ne 0\end{cases}\\\Leftrightarrow \begin{cases}2x\ne\dfrac{\pi}{2}+k2\pi\\x\ne\dfrac{\pi}{2}+k\pi\end{cases}\\\Leftrightarrow \begin{cases}x\ne\dfrac{\pi}{4}+k\pi\\x\ne\dfrac{\pi}{2}+k\pi.\end{cases}\quad(k\in\mathbb{Z})\\TXĐ:D=\mathbb{R}\backslash\left\{\dfrac{\pi}{4}+k\pi;\dfrac{\pi}{2}+k\pi\Big|k\in\mathbb{Z}\right\}.\)
