Nhầm xíu, quên không khai căn, thế này mới đúng :D
\(y=\dfrac{\sqrt{26}}{5}\left(\dfrac{5\sqrt{26}}{26}sinx+\dfrac{\sqrt{26}}{26}cosx\right)=\dfrac{\sqrt{26}}{5}sin\left(x+\alpha\right)\)
Với \(\alpha=arccos\dfrac{5\sqrt{26}}{26}\)
Do \(-1\le sin\left(x+\alpha\right)\le1\Rightarrow\dfrac{-\sqrt{26}}{5}\le y\le\dfrac{\sqrt{26}}{5}\)
\(\Rightarrow\left\{{}\begin{matrix}y_{min}=\dfrac{-\sqrt{26}}{5}\\y_{max}=\dfrac{\sqrt{26}}{5}\end{matrix}\right.\)
\(y=\dfrac{26}{25}\left(\dfrac{25}{26}sinx+\dfrac{5}{26}.cosx\right)=\dfrac{26}{25}sin\left(x+\alpha\right)\) với \(\alpha=arccos\dfrac{25}{26}\)
Do \(-1\le sin\left(x+\alpha\right)\le1\) \(\Rightarrow\dfrac{-26}{25}\le y\le\dfrac{26}{25}\)
\(\Rightarrow y_{min}=-\dfrac{26}{25}\) ; \(y_{max}=\dfrac{26}{25}\)
