Question

giải pt

\(\sqrt{3}cos2x+sin2x+7sinx-\sqrt{3}cosx-3\sqrt{3}=0\)

Answer 1

\(\Leftrightarrow\sqrt{3}\left(1-2sin^2x\right)+2sinx.cosx+7sinx-\sqrt{3}cosx-3\sqrt{3}=0\)

\(\Leftrightarrow cosx\left(2sinx-\sqrt{3}\right)-\left(2\sqrt{3}sin^2x-7sinx+2\sqrt{3}\right)=0\)

\(\Leftrightarrow cosx\left(2sinx-\sqrt{3}\right)-\left(2sinx-\sqrt{3}\right)\left(\sqrt{3}sinx-2\right)=0\)

\(\Leftrightarrow\left(2sinx-\sqrt{3}\right)\left(cosx-\sqrt{3}sinx+2\right)=0\)

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

\(\Leftrightarrow\left(2sinx-\sqrt{3}\right)\left[cos\left(x+\frac{\pi}{3}\right)+1\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=\frac{\sqrt{3}}{2}\\cos\left(x+\frac{\pi}{3}\right)=-1\end{matrix}\right.\)