Question

If y = Tan
V1 + x² + V1 - x?
V1+x? – ſ1 - x²
then find
dy
dx​

Answer 1

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

+θ

⇒y=

4

π

+

2

1

cos

−1

x

2

dx

dy

=0−

2

1

×

1−x

4

1

×2x=−

1−x

4

x