$\begin{array}{l}a) \, y = \dfrac{1 - \sin x}{\cos x}\\ y \,\,\text{xác định}\,\Leftrightarrow \cos x \ne 0\\ \Leftrightarrow x \ne \dfrac{\pi}{2} + k\pi \quad (k \in \Bbb Z)\\ \Rightarrow TXĐ: D = R \backslash\left\{\dfrac{\pi}{2} + k\pi\,|\,k \in \Bbb Z\right\}\\ b)\, y = \sqrt{\dfrac{1 + \sin x}{1 - \sin x}}\\ y \,\,\text{xác định}\,\Leftrightarrow 1 - \sin x \ne 0\\ \Leftrightarrow \sin x \ne 1\\ \Leftrightarrow x \ne \dfrac{\pi}{2} + k2\pi \quad (k \in \Bbb Z)\\ \Rightarrow TXĐ: D = R\backslash\left\{\dfrac{\pi}{2} + l2\pi\,|\,k \in \Bbb Z\right\}\\ c)\, y = \cot\left(x + \dfrac{\pi}{3}\right) - 1\\ y \,\,\text{xác định}\,\Leftrightarrow \sin\left(x + \dfrac{\pi}{3}\right) \ne 0\\ \Leftrightarrow x + \dfrac{\pi}{3} \ne k\pi\\ \Leftrightarrow x \ne - \dfrac{\pi}{3} + k\pi \quad (k \in\Bbb Z)\\ \Rightarrow TXĐ: D =R\backslash\left\{-\dfrac{\pi}{3} + k\pi \,|\, k \in \Bbb Z\right\}\\ d) \, y = 5\tan\left(2x - \dfrac{\pi}{6}\right)\\ y \,\,\text{xác định}\,\Leftrightarrow \cos\left(2x - \dfrac{\pi}{6}\right) \ne 0\\ \Leftrightarrow 2x - \dfrac{\pi}{6} \ne \dfrac{\pi}{2} + k\pi\\ \Leftrightarrow 2x \ne \dfrac{2\pi}{3} + k\pi\\ \Leftrightarrow x \ne \dfrac{\pi}{3} + k\dfrac{\pi}{2} \quad (k \in \Bbb Z)\\ \Rightarrow TXĐ: D = R\backslash\left\{\dfrac{\pi}{3} +k\dfrac{\pi}{2} \,|\,k \in \Bbb Z\right\}\end{array}$
