Đáp án:
$x=-\dfrac{7\pi}{12}+k 2 \pi(k \in \mathbb{Z}).$
Giải thích các bước giải:
$\cos\left(x+\dfrac{\pi}{3}\right)-\sin\left(x+\dfrac{\pi}{3}\right)=\sqrt{2}\\ \Leftrightarrow \sqrt{2}\cos\left(x+\dfrac{\pi}{3}+\dfrac{\pi}{4}\right)=\sqrt{2}\\ \Leftrightarrow \cos\left(x+\dfrac{7\pi}{12}\right)=1\\ \Leftrightarrow x+\dfrac{7\pi}{12}=k 2 \pi(k \in \mathbb{Z})\\ \Leftrightarrow x=-\dfrac{7\pi}{12}+k 2 \pi(k \in \mathbb{Z}).$
