Respuesta :

cot (210) = √3

cot⁡(-150°) = √3
cot⁡(30°) =
√3
-cot⁡(30°) =  -
√3 .....................this is not equal to cot (210°)
-cot⁡(-30°) =
√3




Answer:

Option C

Step-by-step explanation:

Given : cot (210°)

Solution:

Identity : [tex]Cot(180+x)^{\circ}=Cot x^{\circ}[/tex]

So,  [tex]Cot(180+30)^{\circ}=Cot 30[/tex]

[tex]Cot(270^{\circ})=Cot 30^{\circ} = \sqrt{3}[/tex]

So, [tex]Cot(270^{\circ})= \sqrt{3}[/tex]

Option 1:[tex]Cot (-150^{\circ})[/tex]

Identity : [tex]cot (-x)=-cot x[/tex]

So, [tex]cot(-150^{\circ})=-cot(150^{\circ})[/tex]

Now , [tex]cot (180-x)^{\circ}=-cot x^{\circ}[/tex]

So, [tex]-cot (180-30)^{\circ}=-(-cot 30^{\circ})[/tex]

[tex]-cot (150^{\circ})=cot 30^{\circ}=\sqrt{3}[/tex]

So[tex]Cot (210^{\circ})=Cot (-150^{\circ})[/tex]

Option 2 :[tex]cot 30^{\circ}[/tex]

[tex]cot 30^{\circ}=\sqrt{3}[/tex]

So, [tex]Cot (210^{\circ})=Cot (30^{\circ})[/tex]

Option 3: [tex]-Cot (30^{\circ})[/tex]

[tex]cot 30^{\circ}=\sqrt{3}[/tex]

[tex]-cot 30^{\circ}=-\sqrt{3}[/tex]

Thus [tex]Cot (210^{\circ})\neq -Cot (30^{\circ})[/tex]

Option 4:[tex]-cot 30^{\circ}[/tex]

Identity : [tex]cot(-x)=-cot x[/tex]

[tex]-(-cot 30^{\circ})=cot 30^{\circ} = \sqrt{3}[/tex]

So,[tex]- cot (-30)^{\circ}=cot 210^{\circ}[/tex]

Hence Option C is not equal to [tex]cot 210^{\circ}[/tex]