Math, asked by gopisharan498, 6 months ago

if y=tan-¹(1-x²÷1+x²)
then dy/dx is equal to​

Answers

Answered by priyashabaaduwal
0

Answer:

Given y=tan  

−1

(  

1+x  

2

 

​  

−  

1−x  

2

 

​  

 

1+x  

2

 

​  

+  

1−x  

2

 

​  

 

​  

)

Put x  

2

=cos2θ⇒θ=  

2

1

​  

cos  

−1

x  

2

--- (1)

=tan  

−1

(  

1+cos2θ−  

1−cos2θ

​  

 

​  

 

1+cos2θ

​  

+  

1−cos2θ

​  

 

​  

)

⇒tan  

−1

(  

2

​  

cosθ−  

2

​  

sinθ

2

​  

cosθ+  

2

​  

sinθ

​  

)

⇒tan  

−1

(  

1−tanθ

1+tanθ

​  

)

⇒tan  

−1

 

​  

 

1−tan(  

4

π

​  

)tanθ

tan(  

4

π

​  

+tanθ)

​  

 

​  

 

⇒tan  

−1

tan(  

4

π

​  

+θ)=  

4

π

​  

⇒y=  

4

π

​  

+  

2

1

​  

cos  

−1

x  

2

   

dx

dy

​  

=0−  

2

1

​  

×  

1−x  

4

 

​  

 

1

​  

×2x=−  

1−x  

4

 

​  

 

x

​  

 

Step-by-step explanation:

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