Question

Giải pt lượng giác

Answer 1

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=\dfrac{\pi}{3}+k2\pi\\x+\dfrac{\pi}{6}=\pi-\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\left(k\in Z\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\left(k\in Z\right)}\)