1) $5-5\sin x-2{\cos}^2x=0$
$\Rightarrow 5-5\sin x-2(1-{\sin}^2x)=0$
$\Rightarrow 2{\sin}^2x-5\sin x+3=0$
$\Rightarrow \left[ \begin{array}{l} \sin x=\dfrac{3}{2}>1(l) \\ \sin x=1 \end{array} \right .$
$\sin x=1\Rightarrow x=\dfrac{\pi}{2}+k2\pi(k\in\mathbb Z)$
2) $y=\sqrt{\sin x+3}-1$
Ta có: $-1\le\sin x\le1$ $\forall x$
$\Rightarrow -1+3\le\sin x+3\le1+3$
$\Rightarrow 2\le\sin x+3\le 4$
$\Rightarrow\sqrt2\le\sqrt{\sin x+3}\le2$
$\Rightarrow \sqrt2-1\le\sqrt{\sin x+3}-1\le2-1$
$\Rightarrow \sqrt2-1\le y\le 1$
GTLN $y=1$ khi $\sin x=1$
GTNN $y=\sqrt2-1$ khi $\sin x=-1$.
