2sin^2x - 5sinx.cosx - cos^2x

$\begin{array}{l} TH1:\cos x = 0 \Rightarrow {\sin ^2}x = 1,thay\,vao\,pt\,duoc:\\ 2.1 - 5.0 - 0 = 0 \Leftrightarrow 2 = 0\left( {vo\,li} \right)\\ Do\,do\,\cos x = 0\,khong\,thoa\,man\,pt.\\ TH2:\cos x \ne 0,chia\,ca\,hai\,ve\,pt\,cho\,{\cos ^2}x \ne 0\,va\,dat\,\tan x = t\,ta\,co:\\ 2{t^2} - 5t - 1 = 0 \Leftrightarrow t = \frac{{5 \pm \sqrt {33} }}{4}\\ \Rightarrow \tan x = \frac{{5 \pm \sqrt {33} }}{4} \Leftrightarrow x = \arctan \frac{{5 \pm \sqrt {33} }}{4} + k\pi \end{array}$