$$\eqalign{
& \tan x + \cot x = 2 \cr
& \Leftrightarrow \tan x + {1 \over {\tan x}} = 2 \cr
& \Leftrightarrow {\tan ^2}x - 2\tan x + 1 = 0 \cr
& \Leftrightarrow {\left( {\tan x - 1} \right)^2} = 0 \cr
& \Leftrightarrow \tan x = 1 \cr
& \Leftrightarrow x = {\pi \over 4} + k\pi \cr
& \Rightarrow 2\,\,diem\,\,bieu\,dien\,\,M\left( {{{\sqrt 2 } \over 2};{{\sqrt 2 } \over 2}} \right);\,\,N\left( { - {{\sqrt 2 } \over 2}; - {{\sqrt 2 } \over 2}} \right) \cr
& MANA'\,\,la\,\,HCN \cr
& Xet\,\,\Delta OAM:\,\,\widehat {OMA} = {{{{180}^0} - {{45}^0}} \over 2} = {{{{135}^0}} \over 2} \cr
& \Rightarrow \left\{ \matrix{
AN = MN.sin{{{135} \over 2}^0} = 2sin{{{135} \over 2}^0} \hfill \cr
AM = MN.cos{{{135} \over 2}^0} = 2\cos {{{135} \over 2}^0} \hfill \cr} \right. \cr
& \Rightarrow {S_{MANA'}} = AN.AM = 4\sin {{135} \over 2}\cos {{135} \over 2} = 2\sin 135 = \sqrt 2 \cr} $$
