Question

giải phương trình

\(\frac{\cos x-\sqrt{3}\sin x}{2\sin x-1}=0\)

Answer 1

Đk: \(sinx\ne\frac{1}{2}\)

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

\(\Rightarrow cosx-\sqrt{3}sinx=0\)

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

\(\Leftrightarrow sin\frac{\pi}{6}cosx-cos\frac{\pi}{6}sinx=0\)

\(\Leftrightarrow sin\left(\frac{\pi}{6}-x\right)=0\)

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

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

So đk: \(x=\frac{7\pi}{6}+k2\pi\), \(k\in Z\) ( do loại \(k=0,k=2\))