Question

giải phương trình:

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

Answer 1

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

\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sin2x+\dfrac{1}{2}cos2x-\dfrac{1}{2}sinx-\dfrac{\sqrt{3}}{2}cosx+1=0\)

\(\Leftrightarrow sin\left(2x+\dfrac{\pi}{6}\right)-sin\left(x+\dfrac{\pi}{3}\right)+1=0\)

Đặt \(x+\dfrac{\pi}{3}=t\Rightarrow x=t-\dfrac{\pi}{3}\Rightarrow2x+\dfrac{\pi}{6}=2t-\dfrac{\pi}{2}\)

\(\Rightarrow sin\left(2t-\dfrac{\pi}{2}\right)-sint+1=0\)

\(\Leftrightarrow-cos2t-sint+1=0\)

\(\Leftrightarrow2sin^2t-1-sint+1=0\)