Tìm góc nhọn [tex]\dpi{150} \bg_white \alpha[/tex] biết tan [tex]\dpi{150} \bg_white \alpha[/tex] + cot [tex]\dpi{150} \bg_white \alpha[/tex] =2
Có: [tex]tan\alpha +cot\alpha= 2\Leftrightarrow tan\alpha +\frac{1}{tan\alpha }=2[/tex]
[tex]\Leftrightarrow tan^2\alpha +1=2tan\alpha \Leftrightarrow tan^2\alpha -tan\alpha +1=0[/tex]
[tex]\Rightarrow (tan\alpha -1)^2=0\Rightarrow tan\alpha =1=cot\alpha \Rightarrow \alpha =45^0[/tex]