y= sin^4 x + cos^4 x- sin^2 x - cos^2 x .Tìm GTLN GTNN

$y = \sin^4x + \cos^4x - \sin^2x - \cos^2x$

$= (\sin^2 + \cos^2x)^2 -2\sin^2x\cos^2x - (\sin^2x + \cos^2x)$

$= 1 - \dfrac{1}{2}\sin^22x - 1$

$= -\dfrac{1}{2}\sin^22x$

Ta có:

$0 \leq \sin^22x \leq 1$

$-\dfrac{1}{2} \leq -\dfrac{1}{2}\sin^22x \leq 0$

Hay $-\dfrac{1}{2} \leq y \leq 0$

Vậy $\min y = -\dfrac{1}{2} \Leftrightarrow \sin^22x = 1 \Leftrightarrow \sin2x = \pm 1 \Leftrightarrow x = \dfrac{\pi}{4} + k\dfrac{\pi}{2}$

$\max y = 0 \Leftrightarrow \sin2x = 0\Leftrightarrow x = k\dfrac{\pi}{2} \quad (k \in \Bbb Z)$