Bài 1:

1) $\cos\left(x-\dfrac{\pi}{4}\right)=\dfrac{-1}{2}$

$\to x-\dfrac{\pi}{4}=\pm \dfrac{2\pi}{3}+k2\pi$

$\to \left[ \begin{array}{l}x=\dfrac{11\pi}{12}+k2\pi \\x=\dfrac{-5\pi}{12}+k2\pi \end{array} \right.$

Mà $0\le x\le \pi$

$\to x=\dfrac{11\pi}{12}$

2) $\sqrt3\sin3x-\cos3x=\sqrt2$

$\to 2\sin\left(3x-\dfrac{\pi}{6}\right)=\sqrt2$

$\to \sin\left(3x-\dfrac{\pi}{6}\right)=\dfrac{\sqrt2}{2}$

$\to \left[ \begin{array}{l}x=\dfrac{5\pi}{36}+\dfrac{k2\pi}{3} \\x=\dfrac{11\pi}{36}+\dfrac{k2\pi}{3} \end{array} \right.$ 

Bài 2:

a, 

$y=\sin x+\cos x$ có TXĐ $D=\mathbb{R}$

c,

$y=\dfrac{1+\tan x}{\sin x}$

ĐK: $\begin{cases}\sin x\ne 0\\ \cos x\ne 0\end{cases}$

$\to \sin2x=2\sin x\cos x\ne 0$

$\to 2x\ne k\pi$

$\to x\ne k\dfrac{\pi}{2}$

Vậy $D=\mathbb{R}$ \ $\left\{ \dfrac{k\pi}{2}\right\}$

Đáp án:

$\begin{array}{l}
1)\cos \left( {x - \dfrac{\pi }{4}} \right) =  - \dfrac{1}{2}\\
 \Leftrightarrow \left[ \begin{array}{l}
x - \dfrac{\pi }{4} = \dfrac{{2\pi }}{3} + k2\pi \\
x - \dfrac{\pi }{4} =  - \dfrac{{2\pi }}{3} + k2\pi 
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{11\pi }}{{12}} + k2\pi \\
x = \dfrac{{ - 5\pi }}{{12}} + k2\pi 
\end{array} \right.\\
Do:0 \le x \le \pi \\
 \Leftrightarrow x = \dfrac{{11\pi }}{{12}}\\
Vậy\,x = \dfrac{{11\pi }}{{12}}\\
2)\sqrt 3 \sin 3x - \cos 3x = \sqrt 2 \\
 \Leftrightarrow \dfrac{{\sqrt 3 }}{2}\sin 3x - \dfrac{1}{2}\cos 3x = \dfrac{{\sqrt 2 }}{2}\\
 \Leftrightarrow \sin 3x.\cos \dfrac{\pi }{3} - \sin \dfrac{\pi }{3}.\cos 3x = \dfrac{{\sqrt 2 }}{2}\\
 \Leftrightarrow \sin \left( {3x - \dfrac{\pi }{3}} \right) = \dfrac{{\sqrt 2 }}{2}\\
 \Leftrightarrow \left[ \begin{array}{l}
3x - \dfrac{\pi }{3} = \dfrac{\pi }{4} + k2\pi \\
3x - \dfrac{\pi }{3} = \dfrac{{3\pi }}{4} + k2\pi 
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{{7\pi }}{{36}} + \dfrac{{k2\pi }}{3}\\
x = \dfrac{{13\pi }}{{36}} + \dfrac{{k2\pi }}{3}
\end{array} \right.\\
Vậy\,\left[ \begin{array}{l}
x = \dfrac{{7\pi }}{{36}} + \dfrac{{k2\pi }}{3}\\
x = \dfrac{{13\pi }}{{36}} + \dfrac{{k2\pi }}{3}
\end{array} \right.\\
2)a)y = \cos x + \sin x\\
Dkxd:x \in R\\
Vậy\,TXD:D = R\\
b)y = \dfrac{{1 + \tan x}}{{\sin x}}\\
Dkxd:\left\{ \begin{array}{l}
\cos x \ne 0\\
\sin x \ne 0
\end{array} \right.\\
 \Leftrightarrow 2\sin x.\cos x \ne 0\\
 \Leftrightarrow \sin 2x \ne 0\\
 \Leftrightarrow 2x \ne k\pi \\
 \Leftrightarrow x \ne \dfrac{{k\pi }}{2}\\
Vậy\,TXD:D = R\backslash \left\{ {\dfrac{{k\pi }}{2};k \in Z} \right\}
\end{array}$