Cho cot α= $\sqrt{5}$ . Tính C= `sin^2 α-sinα.cosα+cos^2α`

   $\text{Cot$\alpha$=$\sqrt{5}$}$

⇒$\text{Cot²$\alpha$=5}$

⇒$\text{1+Cot²$\alpha$=$\dfrac{1}{Sin²\alpha}$=6}$

⇒$\text{Sin$\alpha$=$\dfrac{\sqrt{6}}{6}$}$

Mà : $\text{Sin²$\alpha$+Cos²$\alpha$=1}$

⇒$\text{Cos$\alpha$=$\dfrac{\sqrt{30}}{6}$}$

Ta có :

$\text{C=Sin²$\alpha$-Sin$\alpha$·Cos$\alpha$+Cos²$\alpha$}$

$\text{C=1-Sin$\alpha$·Cos$\alpha$}$

$\text{C=1-($\dfrac{\sqrt{6}}{6}$}·\dfrac{\sqrt{30}}{6})=\dfrac{6-\sqrt{5}}{6}$

$\text{Vậy với Cot$\alpha$=$\sqrt{5}$ ⇒ C=$\dfrac{6-\sqrt{5}}{6}$}$