Question

dy
If y = cot
1-37
3r-
dy
3
1+
1-2
1
(C)
1
1+
3(1+*?)​

Answer 1

Answer:

Step-by-step explanation:

We have,

y=cot  

−1

(  

3x−x  

3

 

1−3x  

2

 

​  

);∣x∣>  

3

​  

 

1

​  

 

Put x=cotθ⇒θ=cot  

−1

x

Then,

Put and we get,

y=cot  

−1

(  

3cotθ−cot  

3

θ

1−3cot  

2

θ

​  

)

y=tan  

−1

(  

1−3cot  

2

θ

3cotθ−cot  

3

θ

​  

)

=tan  

−1

(  

3cot  

2

θ−1

cot  

3

θ−3cotθ

​  

)

=tan  

−1

cot3θ

=tan  

−1

tan(  

2

π

​  

−3θ)

=  

2

π

​  

−3θ

y=  

2

π

​  

−3cot  

−1

x

On differentiating and we get,

dx

dy

​  

=  

dx

d

​  

(  

2

π

​  

−3cot  

−1

x)

=(0−3(−  

1+x  

2

 

1

​  

))

=  

1+x  

2

 

3

​  

 

Hence, this is the answer.