Đáp án:
Giải thích các bước giải:
`sin x+\sqrt{3}cos x=\sqrt{2}`
`⇔ 1/2 sin x+\frac{\sqrt{3}}{2} cos x=\frac{\sqrt{2}}{2}`
`⇔ sin (x+\frac{\pi}{3})=sin \frac{\pi}{4}`
`⇔` \(\left[ \begin{array}{l}x+\dfrac{\pi}{3})= \dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\\x+\dfrac{\pi}{3})=\pi-\dfrac{\pi}{4}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=-\dfrac{\pi}{12}+k2\pi\ (k \in \mathbb{Z})\\x=\dfrac{5\pi}{12}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
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