\(y=\sqrt{3}cosx-sinx=2\left(\dfrac{\sqrt{3}}{2}cosx-\dfrac{1}{2}sinx\right)=2cos\left(x+\dfrac{\pi}{6}\right)\)

Vì \(cos\left(x+\dfrac{\pi}{6}\right)\in\left[-1;1\right]\Rightarrow y=\sqrt{3}cosx-sinx\in\left[-2;2\right]\)

\(\Rightarrow y_{min}=-2\Leftrightarrow cos\left(x+\dfrac{\pi}{6}\right)=-1\Leftrightarrow x+\dfrac{\pi}{6}=\pi+k2\pi\Leftrightarrow x=\dfrac{5\pi}{6}+k2\pi\)

\(y_{max}=2\Leftrightarrow cos\left(x+\dfrac{\pi}{6}\right)=1\Leftrightarrow x+\dfrac{\pi}{6}=k2\pi\Leftrightarrow x=-\dfrac{\pi}{6}+k2\pi\)

Chọn B

Chọn C

\(y=\left|2sin^2x-sinx-1\right|-2sinx\)

Đặt \(sinx=t\in\left[-1;1\right]\)

\(\Rightarrow y=f\left(t\right)=\left|2t^2-t-1\right|-2t\)

BBT cho \(f\left(t\right)\) trên \(\left[-1;1\right]\):

Từ BBT ta thấy \(y_{max}=4\) khi \(sinx=-1\); \(y_{min}=-2\) khi \(sinx=1\)

Đặt \(sinx+cosx=t\Rightarrow-\sqrt{2}\le t\le\sqrt{2}\)

\(t^2=sin^2x+cos^2x+2sinx.cosx=1+2sinx.cosx\Rightarrow sinx.cosx=\dfrac{t^2-1}{2}\)

\(\Rightarrow y=t+\dfrac{t^2-1}{2}=\dfrac{1}{2}t^2+t-\dfrac{1}{2}\)

Xét hàm \(f\left(t\right)=\dfrac{1}{2}t^2+t-\dfrac{1}{2}\) trên \(\left[-\sqrt{2};\sqrt{2}\right]\)

\(-\dfrac{b}{2a}=-1\) 

\(f\left(-\sqrt{2}\right)=\dfrac{1-2\sqrt{2}}{2}\) ; \(f\left(-1\right)=-1\) ; \(f\left(\sqrt{2}\right)=\dfrac{1+2\sqrt{2}}{2}\)

\(\Rightarrow y_{min}=-1\) khi \(t=-1\) ; \(y_{max}=\dfrac{1+2\sqrt{2}}{2}\) khi \(t=\sqrt{2}\)

Đặt \(t=sinx+cosx;t\in\left[-\sqrt{2};\sqrt{2}\right]\)

\(\Rightarrow\dfrac{t^2-1}{2}=sinx.cosx\)

\(y=t+\dfrac{t^2-1}{2}=\dfrac{t^2}{2}+t-\dfrac{1}{2}\)

Vẽ BBT của \(f\left(t\right)=\dfrac{t^2}{2}+t-\dfrac{1}{2};t\in\left[-\sqrt{2};\sqrt{2}\right]\)

\(\Rightarrow\)\(f\left(t\right)_{min}=-1\Leftrightarrow t=-1\Rightarrow sinx+cosx=-1\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=-\dfrac{1}{\sqrt{2}}\)....

\(f\left(t\right)_{max}=\dfrac{1+2\sqrt{2}}{2}\)\(\Leftrightarrow t=\sqrt{2}\Rightarrow sinx+cosx=\sqrt{2}\Leftrightarrow sin\left(x+\dfrac{\pi}{4}\right)=1\)....

Đáp án C

Đặt \(sinx=t\left(t\in\left[-1;1\right]\right)\)

\(y=\left|sinx+cos2x\right|=\left|2sin^2x-sinx-1\right|\)

\(\Leftrightarrow y=\left|f\left(t\right)\right|=\left|2t^2-t-1\right|\)

\(f\left(-1\right)=2\Rightarrow y=2\)

\(f\left(1\right)=0\Rightarrow y=0\)

\(f\left(\dfrac{1}{4}\right)=-\dfrac{9}{8}\Rightarrow y=\dfrac{9}{8}\)

\(\Rightarrow y_{min}=0;y_{max}=2\)