Đáp án:

\(\begin{array}{l}
15,\\
D = \left( { - \infty ;1} \right] \cup \left[ {2; + \infty } \right)\\
16,\\
D = R\backslash \left\{ {\dfrac{\pi }{2} + k\pi ;\dfrac{\pi }{4} + k\pi |k \in Z} \right\}\\
17,\\
D = R\\
19,\\
D = R\backslash \left\{ {\dfrac{{k\pi }}{2}|k \in Z} \right\}\\
20,\\
D = R\backslash \left\{ {\dfrac{\pi }{3} + k\pi ;k2\pi |k \in Z} \right\}\\
21,\\
D = R\backslash \left\{ {\dfrac{{k\pi }}{2}; - \dfrac{\pi }{4} + k\pi |k \in Z} \right\}\,
\end{array}\)

Giải thích các bước giải:

 Các hàm số đã cho xác định khi và chỉ khi:

\(\begin{array}{l}
15,\\
{x^2} - 3x + 2 \ge 0\\
 \Leftrightarrow \left( {{x^2} - 2x} \right) + \left( { - x + 2} \right) \ge 0\\
 \Leftrightarrow x\left( {x - 2} \right) - \left( {x - 2} \right) \ge 0\\
 \Leftrightarrow \left( {x - 2} \right)\left( {x - 1} \right) \ge 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x \ge 2\\
x \le 1
\end{array} \right.\\
 \Rightarrow TXD:\,\,\,\,D = \left( { - \infty ;1} \right] \cup \left[ {2; + \infty } \right)\\
16,\\
\left\{ \begin{array}{l}
\cos x \ne 0\\
\tan x - 1 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\cos x \ne 0\\
\tan x \ne 1
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{2} + k\pi \\
x \ne \dfrac{\pi }{4} + k\pi 
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\\
 \Rightarrow TXD:\,\,\,D = R\backslash \left\{ {\dfrac{\pi }{2} + k\pi ;\dfrac{\pi }{4} + k\pi |k \in Z} \right\}\\
17,\\
{\sin ^2}x - 2\cos x + 4 \ne 0\\
 \Leftrightarrow \left( {1 - {{\cos }^2}x} \right) - 2\cos x + 4 \ne 0\\
 \Leftrightarrow 1 - {\cos ^2}x - 2\cos x + 4 \ne 0\\
 \Leftrightarrow  - {\cos ^2}x - 2\cos x + 5 \ne 0\\
 \Leftrightarrow {\cos ^2}x + 2\cos x - 5 \ne 0\\
 \Leftrightarrow {\cos ^2}x + 2\cos x + 1 \ne 6\\
 \Leftrightarrow {\left( {\cos x + 1} \right)^2} \ne 6\\
 - 1 \le \cos x \le 1\\
 \Leftrightarrow 0 \le \cos x + 1 \le 2\\
 \Leftrightarrow 0 \le {\left( {\cos x + 1} \right)^2} \le 4\\
 \Rightarrow {\left( {\cos x + 1} \right)^2} \ne 6,\,\,\,\forall x\\
 \Rightarrow TXD:\,\,\,D = R\\
19,\\
\left\{ \begin{array}{l}
\cos x \ne 0\\
\tan x \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\cos x \ne 0\\
\sin x \ne 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{2} + k\pi \\
x \ne k\pi 
\end{array} \right. \Leftrightarrow x \ne \dfrac{{k\pi }}{2}\,\,\,\,\left( {k \in Z} \right)\\
 \Rightarrow TXD:\,\,\,\,D = R\backslash \left\{ {\dfrac{{k\pi }}{2}|k \in Z} \right\}\\
20,\\
\left\{ \begin{array}{l}
\sin \left( {x - \dfrac{\pi }{3}} \right) \ne 0\\
1 - \cos x \ge 0\\
\sqrt {1 - \cos x}  \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x - \dfrac{\pi }{3} \ne k\pi \\
\cos x \le 1,\,\,\,\forall x\\
\cos x \ne 1
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{3} + k\pi \\
\cos x \ne 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{\pi }{3} + k\pi \\
x \ne k2\pi 
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\\
 \Rightarrow TXD:\,\,\,\,D = R\backslash \left\{ {\dfrac{\pi }{3} + k\pi ;k2\pi |k \in Z} \right\}\\
21,\\
\left\{ \begin{array}{l}
\sin 2x \ne 0\\
\sin \left( {x + \dfrac{\pi }{4}} \right) \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
2x \ne k\pi \\
x + \dfrac{\pi }{4} \ne k\pi 
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x \ne \dfrac{{k\pi }}{2}\\
x \ne  - \dfrac{\pi }{4} + k\pi 
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)\\
 \Rightarrow TXD:\,\,\,D = R\backslash \left\{ {\dfrac{{k\pi }}{2}; - \dfrac{\pi }{4} + k\pi |k \in Z} \right\}\,
\end{array}\)