\(y=-sin\left(x+\dfrac{\pi}{6}\right)+\sqrt{3}cos\left(x+\dfrac{\pi}{6}\right)+1\)
\(=2\left[-\dfrac{1}{2}sin\left(x+\dfrac{\pi}{6}\right)+\dfrac{\sqrt{3}}{2}cos\left(x+\dfrac{\pi}{6}\right)\right]+1\)
\(=2cos\left(x+\dfrac{\pi}{3}\right)+1\)
Vì \(cos\left(x+\dfrac{\pi}{3}\right)\in\left[-1;1\right]\Rightarrow y=2cos\left(x+\dfrac{\pi}{3}\right)+1\in\left[-1;3\right]\)
\(\Rightarrow\left\{{}\begin{matrix}y_{min}=-1\\y_{max}=3\end{matrix}\right.\)
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