$y = 5 - 2\sin^2x$
Ta có:
$0 \leq \sin^2x \leq 1$
$\Leftrightarrow -2 \leq -2\sin^2x \leq 0$
$\Leftrightarrow 3 \leq 5 - 2\sin^2x \leq 5$
Hay $3 \leq y \leq 5$
Vậy $\min y = 3 \Leftrightarrow \sin x = 0 \Leftrightarrow x = k\pi$
$\max y = 5 \Leftrightarrow \sin x = \pm 1 \Leftrightarrow x = \dfrac{\pi}{2} + k\pi\quad (k\in \Bbb Z)$