Question

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

cot⁡(-150°)
cot⁡(30°)
-cot⁡(30°)
-cot⁡(-30°)

Answer 1

Option C

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) = √(3)`

So,
`Cot(270^(\circ))= √(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)=√(3)`

So
`Cot (210^(\circ))=Cot (-150^(\circ))`

Option 2 :
`cot 30^(\circ)`

`cot 30^(\circ)=√(3)`

So,
`Cot (210^(\circ))=Cot (30^(\circ))`

Option 3:
`-Cot (30^(\circ))`

`cot 30^(\circ)=√(3)`

`-cot 30^(\circ)=-√(3)`

Thus
`Cot (210^(\circ))\\eq -Cot (30^(\circ))`

Option 4:
`-cot 30^(\circ)`

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

`-(-cot 30^(\circ))=cot 30^(\circ) = √(3)`

So,
`- cot (-30)^(\circ)=cot 210^(\circ)`

Hence Option C is not equal to
`cot 210^(\circ)`

Answer 2

cot (210) = √3

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