`~rai~`
\(\sin x+\cos(\pi-x)=1\\\Leftrightarrow \sin x-\cos x=1\\\Leftrightarrow \sqrt{2}\left(\dfrac{\sqrt{2}}{2}\sin x-\dfrac{\sqrt{2}}{2}\cos x\right)=1\\\Leftrightarrow \sin\left(x-\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{2}\\\Leftrightarrow \left[\begin{array}{I}x-\dfrac{\pi}{4}=\dfrac{\pi}{4}+k2\pi\\x-\dfrac{\pi}{4}=\pi-\dfrac{\pi}{4}+k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=\dfrac{\pi}{2}+k2\pi\\x=\pi++k2\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Vậy S}=\left\{\dfrac{\pi}{2}+k2\pi;\pi+k2\pi\Big|k\in\mathbb{Z}\right\}.\)
