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