a.
\(-1\le sin\left(x+\dfrac{\pi}{4}\right)\le1\Rightarrow-1\le y\le3\)
\(y_{min}=-1\) khi \(sin\left(x+\dfrac{\pi}{4}\right)=1\Rightarrow x=\dfrac{\pi}{4}+k2\pi\)
\(y_{max}=3\) khi \(sin\left(x+\dfrac{\pi}{4}\right)=-1\Rightarrow x=-\dfrac{3\pi}{4}+k2\pi\)
b.
\(0\le cos^23x\le1\Rightarrow2\le y\le3\)
\(y_{min}=2\) khi \(cos^23x=1\Rightarrow x=\dfrac{k\pi}{3}\)
\(y_{max}=3\) khi \(cos^23x=0\Rightarrow x=\dfrac{\pi}{6}+\dfrac{k\pi}{3}\)
c.
\(y=1-sin^2x+sinx+2=-sin^2x+sinx+3\)
Đặt \(sinx=t\in\left[-1;1\right]\) \(\Rightarrow y=f\left(t\right)=-t^2+t+3\)
\(-\dfrac{b}{2a}=\dfrac{1}{2}\in\left[-1;1\right]\)
\(f\left(-1\right)=1\) ; \(f\left(\dfrac{1}{2}\right)=\dfrac{13}{4}\); \(f\left(1\right)=3\)
\(\Rightarrow y_{min}=1\) khi \(sinx=-1\Rightarrow x=-\dfrac{\pi}{2}+k2\pi\)
\(y_{max}=\dfrac{13}{4}\) khi \(sinx=\dfrac{1}{2}\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
