Question

giải phương trình

\(\sqrt{3}sin2x+cos2x=2cosx-1\)

Answer 1

\(\Leftrightarrow2\sqrt{3}.sinx.cosx+2cos^2x-1=2cosx-1\)

\(\Leftrightarrow\sqrt{3}sinx.cosx+cos^2x-cosx=0\)

\(\Leftrightarrow cosx\left(\sqrt{3}sinx+cosx-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\\frac{\sqrt{3}}{2}sinx+\frac{1}{2}cosx=\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sin\left(x+\frac{\pi}{6}\right)=\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow...\)