Question

Giải phương trình sau:

a)sinx+\(\sqrt{3}cosx=2sin3x\)

Answer 1

\(\Leftrightarrow\dfrac{1}{2}sinx+\dfrac{\sqrt{3}}{2}cosx=sin3x\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{3}\right)=sin3x\)

\(\Leftrightarrow\left[{}\begin{matrix}3x=x+\dfrac{\pi}{3}+k2\pi\\3x=\dfrac{2\pi}{3}-x+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k\pi\\x=\dfrac{\pi}{6}+\dfrac{k\pi}{2}\end{matrix}\right.\)

\(\Leftrightarrow x=\dfrac{\pi}{6}+\dfrac{k\pi}{2}\)