`~rai~`
\(d)y=\sqrt{5-2\cos^2x\sin^2x}\\\quad=\sqrt{5-\dfrac{1}{2}.4\sin^2x\cos^2x}\\\quad=\sqrt{5-\dfrac{1}{2}\sin^22x}.\\\text{Ta có:}0\le\sin^22x\le1\\\Leftrightarrow -\dfrac{1}{2}\le-\dfrac{1}{2}\sin^22x\le0\\\Leftrightarrow \dfrac{9}{2}\le5-\dfrac{1}{2}\sin^22x\le5\\\Leftrightarrow \sqrt{\dfrac{9}{2}}\le\sqrt{5-\dfrac{1}{2}\sin^22x}\le\sqrt{5}\\\Leftrightarrow \dfrac{3\sqrt{2}}{2}\le y\le\sqrt{5}.\\\Leftrightarrow Min_y=\dfrac{3\sqrt{2}}{2};Max_y=\sqrt{5}.\\+)Min_y=\dfrac{3\sqrt{2}}{2}\Leftrightarrow \sin^22x=1\Leftrightarrow \sin2x=\pm1\Leftrightarrow x=\pm\dfrac{\pi}{4}+k\pi.(k\in\mathbb{Z})\\+)Max_y=\sqrt{5}\Leftrightarrow \sin^22x=0\Leftrightarrow \sin2x=0\Leftrightarrow x=k\dfrac{\pi}{2}.(k\in\mathbb{Z})\)
