Đáp án:
$ x\in \left\{\dfrac{-3\pi}{4};\dfrac{-5\pi}{12};\dfrac{-\pi}{12};\dfrac{\pi}{4};\dfrac{7\pi}{12};\dfrac{11\pi}{12};\dfrac{5\pi}{4};\dfrac{19\pi}{12};\dfrac{23\pi}{12};\dfrac{9\pi}{4};\dfrac{31\pi}{12};\dfrac{35\pi}{12};\dfrac{-15\pi}{16};\dfrac{-15\pi}{16};\dfrac{-11\pi}{16};\dfrac{-7\pi}{16};\dfrac{-3\pi}{16};\dfrac{\pi}{16};\dfrac{5\pi}{16};\dfrac{9\pi}{16};\dfrac{13\pi}{16};\dfrac{17\pi}{16};\dfrac{21\pi}{16};\dfrac{25\pi}{16};\dfrac{29\pi}{16};\dfrac{33\pi}{16};\dfrac{37\pi}{16};\dfrac{41\pi}{16};\dfrac{45\pi}{16}\right\}$
Giải thích các bước giải:
$b)\sin x= \cos 7x\\ \sin x= \sin\left(7x+\dfrac{\pi}{2}\right)\\ \Leftrightarrow \left[\begin{array}{l} x=7x+\dfrac{\pi}{2}+k 2 \pi( k \in \mathbb{Z} )\\ x=\pi-7x-\dfrac{\pi}{2}+k 2 \pi( k \in \mathbb{Z}) \end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} -6x=\dfrac{\pi}{2}+k 2 \pi( k \in \mathbb{Z})\\ 8x=\dfrac{\pi}{2}+k 2 \pi( k \in \mathbb{Z}) \end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} x=-\dfrac{\pi}{12}-\dfrac{k \pi}{3}( k \in \mathbb{Z} )\\ x=\dfrac{\pi}{16}+\dfrac{k \pi}{4}( k \in \mathbb{Z} )\end{array} \right.\\ x \in [-\pi,3 \pi]\\ \Rightarrow x\in \left\{\dfrac{-3\pi}{4};\dfrac{-5\pi}{12};\dfrac{-\pi}{12};\dfrac{\pi}{4};\dfrac{7\pi}{12};\dfrac{11\pi}{12};\dfrac{5\pi}{4};\dfrac{19\pi}{12};\dfrac{23\pi}{12};\dfrac{9\pi}{4};\dfrac{31\pi}{12};\dfrac{35\pi}{12};\dfrac{-15\pi}{16};\dfrac{-15\pi}{16};\dfrac{-11\pi}{16};\dfrac{-7\pi}{16};\dfrac{-3\pi}{16};\dfrac{\pi}{16};\dfrac{5\pi}{16};\dfrac{9\pi}{16};\dfrac{13\pi}{16};\dfrac{17\pi}{16};\dfrac{21\pi}{16};\dfrac{25\pi}{16};\dfrac{29\pi}{16};\dfrac{33\pi}{16};\dfrac{37\pi}{16};\dfrac{41\pi}{16};\dfrac{45\pi}{16}\right\}$
