a/ \(y=2cos\left(\frac{\pi}{14}\right)cos\left(x-\frac{\pi}{14}\right)\)
Do \(-1\le cos\left(x-\frac{\pi}{14}\right)\le1\) với mọi x
\(\Rightarrow-2cos\left(\frac{\pi}{14}\right)\le y\le2cos\left(\frac{\pi}{14}\right)\)
\(y_{min}=-2cos\left(\frac{\pi}{14}\right)\) khi \(cos\left(x-\frac{\pi}{14}\right)=-1\)
\(y_{max}=2cos\left(\frac{\pi}{14}\right)\) khi \(cos\left(x-\frac{\pi}{14}\right)=1\)
b/ \(y=\sqrt{3}cos2x-\frac{1}{2}sin2x=\frac{\sqrt{13}}{2}\left(\frac{2\sqrt{39}}{13}cos2x-\frac{\sqrt{13}}{13}sin2x\right)\)
\(\Rightarrow y=\frac{\sqrt{13}}{2}cos\left(2x+a\right)\) với \(a\in\left(0;\pi\right)\) sao cho \(cosa=\frac{2\sqrt{39}}{13}\)
Do \(-1\le cos\left(2x+a\right)\le1\Rightarrow-\frac{\sqrt{13}}{2}\le y\le\frac{\sqrt{13}}{2}\)
c/ \(y=4sin^2x+4sinx+1+4cos^2x-4\sqrt{3}cosx+3\)
\(=8+4sinx-4\sqrt{3}cosx=8+8\left(\frac{1}{2}sinx-\frac{\sqrt{3}}{2}cosx\right)\)
\(=8+8sin\left(x-\frac{\pi}{3}\right)\)
Do \(-1\le sin\left(x-\frac{\pi}{3}\right)\le1\Rightarrow0\le y\le16\)
