Đáp án:
\(\left[ \begin{array}{l}x=\dfrac{\pi}{12}+k.2\pi\\x=\dfrac{7\pi}{12} +k.2\pi\end{array} \right.\) \((k \epsilon Z)\)
Giải thích các bước giải:
\(\sqrt{3} \sin x +\cos x=\sqrt{2}\)
\(\Leftrightarrow \dfrac{\sqrt{3}}{2}.\sin x+\dfrac{1}{2}.\cos x=\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow \cos \dfrac{\pi}{6}.\sin x+\sin \dfrac{\pi}{6}.\cos x=\sin \dfrac{\pi}{4}\)
\(\Leftrightarrow \sin (x+\dfrac{\pi}{6})=\sin \dfrac{\pi}{4}\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}x+\dfrac{\pi}{6}=\dfrac{\pi}{4}+k.2\pi\\x+\dfrac{\pi}{6}=\pi-\dfrac{\pi}{4} +k.2\pi\end{array} \right.\)
\(\Leftrightarrow \) \(\left[ \begin{array}{l}x=\dfrac{\pi}{12}+k.2\pi\\x=\dfrac{7\pi}{12} +k.2\pi\end{array} \right.\) \((k \epsilon Z)\)
