Question

sec^-1 underoot 1+4x² inverse trigonometry derivative

Answer 1

Answer:

Solution

verified

Verified by Toppr

Let y=cos

−1

(2x

1−x

2

)

Put x=sinθ

∴θ=sin

−1

x

⇒y=cos

−1

(2sinθ

1−sin

2

θ)

⇒y=cos

−1

(2sinθcosθ)

⇒y=cos

−1

(sin2θ)

⇒y=cos

−1

[cos(

2

π

−2θ)]

⇒y=

2

π

−2θ

⇒y=

2

π

−2sin

−1

x

⇒

dx

dy

=

1−x

2

−2