Question

Which of the following is not equal to cot⁡(210°)?

Answer 1

Cot (210) = √3

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

Answer 2

Answer:

Option C

Step-by-step explanation:

Given : cot (210°)

Solution:

Identity : $Cot(180+x)^{\circ}=Cot x^{\circ}$

So,  $Cot(180+30)^{\circ}=Cot 30$

$Cot(270^{\circ})=Cot 30^{\circ} = \sqrt{3}$

So, $Cot(270^{\circ})= \sqrt{3}$

Option 1:$Cot (-150^{\circ})$

Identity : $cot (-x)=-cot x$

So, $cot(-150^{\circ})=-cot(150^{\circ})$

Now , $cot (180-x)^{\circ}=-cot x^{\circ}$

So, $-cot (180-30)^{\circ}=-(-cot 30^{\circ})$

$-cot (150^{\circ})=cot 30^{\circ}=\sqrt{3}$

So$Cot (210^{\circ})=Cot (-150^{\circ})$

Option 2 :$cot 30^{\circ}$

$cot 30^{\circ}=\sqrt{3}$

So, $Cot (210^{\circ})=Cot (30^{\circ})$

Option 3: $-Cot (30^{\circ})$

$cot 30^{\circ}=\sqrt{3}$

$-cot 30^{\circ}=-\sqrt{3}$

Thus $Cot (210^{\circ})\neq -Cot (30^{\circ})$

Option 4:$-cot 30^{\circ}$

Identity : $cot(-x)=-cot x$

$-(-cot 30^{\circ})=cot 30^{\circ} = \sqrt{3}$

So,$- cot (-30)^{\circ}=cot 210^{\circ}$

Hence Option C is not equal to $cot 210^{\circ}$