Đáp án:
$$\left[ \matrix{
x = {\pi \over 4} + k\pi \hfill \cr
x = \arctan \left( { - 3} \right) + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right)$$
Giải thích các bước giải:
$$\eqalign{
& {\sin ^2}x + 2\sin x\cos x - 3{\cos ^2}x = 0 \cr
& TH1:\,\,\cos x = 0 \Leftrightarrow {\sin ^2}x = 1 \cr
& \Rightarrow 1 = 0\,\,\left( {Vo\,\,nghiem} \right) \cr
& TH2:\,\,\cos x \ne 0 \Leftrightarrow x \ne {\pi \over 2} + k\pi \cr
& PT:\,\,{\tan ^2}x + 2\tan x - 3 = 0 \cr
& \Leftrightarrow \left[ \matrix{
\tan x = 1 \hfill \cr
\tan x = - 3 \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
x = {\pi \over 4} + k\pi \hfill \cr
x = \arctan \left( { - 3} \right) + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr} $$
