tìm m để hàm số y= $\sqrt[]{2sin^2x+4sinxcosx-(3+2m)cos^2x+2}$ xác định với mọi x

\[\begin{array}{l} y = \sqrt {2{{\sin }^2}x + 4\sin x\cos x - \left( {3 + 2m} \right){{\cos }^2}x + 2} \\ Ham\,\,so\,\,xd\,\,voi\,\,moi\,\,x\\ \Leftrightarrow f\left( x \right) = 2{\sin ^2}x + 4\sin x\cos x - \left( {3 + 2m} \right){\cos ^2}x + 2 \ge 0\,\,\forall x\,\\ Voi\,\,\cos x = 0\\ \Rightarrow f\left( x \right) = 2{\sin ^2}x + 2 > 0\,\,\\ \Rightarrow \cos x = 0\,\,khong\,\,la\,\,nghiem\,\,cua\,pt\,\,f\left( x \right) = 0.\\ Chia\,\,ca\,\,2\,\,ve\,\,cua\,\,\left( * \right)\,cho\,\,{\cos ^2}x\,\,ta\,\,duoc:\\ 2{\tan ^2}x + 4\tan x - 3 - 2m + \frac{2}{{{{\cos }^2}x}} \ge 0\,\,\forall x\\ \Leftrightarrow \,\,2{\tan ^2}x + 4\tan x - 3 - 2m + 2{\tan ^2}t + 2 \ge 0\,\,\forall t\\ \Leftrightarrow 4{\tan ^2}x + 4\tan x - 1 - 2m \ge 0\,\,\,\,\,\forall t\,\,\left( 1 \right)\\ Dat\,\,\tan \,x = t\\ \Rightarrow \left( 1 \right) \Leftrightarrow 4{t^2} + 4y - 2m - 1 \ge 0\,\,\forall t\\ \Leftrightarrow \Delta ' \le 0 \Leftrightarrow 4 + 4\left( {2m + 1} \right) \le 0\\ \Leftrightarrow 1 + 2m + 1 \le 0\\ \Leftrightarrow 2m \le - 2\\ \Leftrightarrow m \le - 1. \end{array}\]