Question

gpt

\(\frac{cosx-\sqrt{3}sinx}{sinx-\frac{1}{2}}=0\)

Answer 1

ĐKXĐ: \(sinx\ne\frac{1}{2}\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{6}+k2\pi\\x\ne\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)

Pt tương đương:

\(cosx=\sqrt{3}sinx\Leftrightarrow tanx=\frac{1}{\sqrt{3}}\)

\(\Leftrightarrow x=\frac{\pi}{6}+k\pi\)

Kết hợp ĐKXĐ \(\Rightarrow x=\frac{7\pi}{6}+k2\pi\)