Đáp án:
Giải thích các bước giải:
`\sqrt{3}tan^2 x-(1+\sqrt{3})tan\ x+1=0`
`⇔ (tan\ x-1)(\sqrt{3}tan\ x-1)=0`
`⇔` \(\left[ \begin{array}{l}\tan\ x-1=0\\\sqrt{3}\tan\ x-1=0\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}\tan\ x=1\\\tan\ x=\dfrac{\sqrt{3}}{3}\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=\dfrac{\pi}{4}+k\pi\ (k \in \mathbb{Z})\\x=\dfrac{\pi}{6}+k\pi\ (k \in \mathbb{Z})\end{array} \right.\)
Vậy `S={\frac{\pi}{4}+k\pi\ (k \in \mathbb{Z});\frac{\pi}{6}+k\pi\ (k \in \mathbb{Z})}`
