Question

Find the differential coefficient of tan^-1(x/√(1-x^2))
with respect to
sec^-1 (1/((2x^2) -1)).


​

Answer 1

answers:

For the first one let x=tanA

Therefore upon simplification we get that

cot

−1

(

x

1+x

2

−1

)

=cot

−1

tan(A/2)

=

2

π

−

2

A

=

2

π−tan

−1

x

=u ...(i)

Substituting x=cosB in the second one and simplifying we get

tan

−1

(tan2B)

=2A

=2cos

1

x

=v

Hence

dv

du

=

dx

dv

dx

du

=

1−x

2

−2

1+x

2

−1

=

4(1+x

2

)

1−x

2