a, \(y=sinx+\sqrt{3}cosx=2sin\left(x+\dfrac{\pi}{3}\right)\)
Vì \(sin\left(x+\dfrac{\pi}{3}\right)\in\left[-1;1\right]\Rightarrow y=2sin\left(x+\dfrac{\pi}{3}\right)\in\left[-2;2\right]\)
b, \(y=sin2x+cos2x+1=\sqrt{2}sin\left(2x+\dfrac{\pi}{4}\right)+1\)
Vì \(sin\left(2x+\dfrac{\pi}{4}\right)\in\left[-1;1\right]\Rightarrow y=\sqrt{2}sin\left(2x+\dfrac{\pi}{4}\right)+1\in\left[1-\sqrt{2};2+\sqrt{2}\right]\)
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