Question

Giải PT:

\(2\left(\sqrt{3}sinx-cosx\right)=3sin2x+\sqrt{7}cos2x\)

Answer 1

\(\Leftrightarrow\dfrac{\sqrt{3}}{2}\sin x-\dfrac{1}{2}\cos x=\dfrac{3}{4}\sin2x+\dfrac{\sqrt{7}}{4}\cos2x\)

\(\Leftrightarrow\sin\left(x-\dfrac{\Pi}{6}\right)=\sin\left(2x+\alpha\right)\) với cos a=3/4; sin a=căn 7/4

\(\Leftrightarrow\left\{{}\begin{matrix}x-\dfrac{\Pi}{6}=2x+a+k2\Pi\\x-\dfrac{\Pi}{6}=-2x-a+\Pi+k2\Pi\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-x=a+k2\Pi+\dfrac{\Pi}{6}\\3x=\dfrac{7}{6}\Pi-a+k2\Pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-a-k2\Pi-\dfrac{\Pi}{6}\\x=\dfrac{7}{18}\Pi-\dfrac{a}{3}+\dfrac{k2\Pi}{3}\end{matrix}\right.\)