Đáp án:
Giải thích các bước giải:
`sin\ x+\sqrt{3}cos\ x=1`
`⇔ \frac{1}{\sqrt{(\sqrt{3})^2+1^2}}sin\ x+\frac{\sqrt{3}}{\sqrt{(\sqrt{3})^2+1^2}}cos\ x=\frac{1}{\sqrt{(\sqrt{3})^2+1^2}}`
`⇔ \frac{1}{2}sin\ x+\frac{\sqrt{3}}{2}cos\ x=\frac{1}{2}`
`⇔ cos\ \frac{\pi}{3} . sin\ x+sin\ \frac{\pi}{3} . cos\ x=\frac{1}{2}`
`⇔ sin\ (x+\frac{\pi}{3})=1/2`
`⇔ sin\ (x+\frac{\pi}{3})=sin\ \frac{\pi}{6}`
`⇔` \(\left[ \begin{array}{l}x=-\dfrac{\pi}{6}+k2\pi\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{2}+k2\pi\ (k \in \mathbb{Z})\end{array} \right.\)
