tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(...

`tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))`

A

`(pi)/(4)-(1)/(2) cos^(-1)x`

B

`(pi)/(4) +cos^(-1)x^(2) `

C

`(pi)/(4) +(1)/(2) cos^(-1)x^(2)`

D

`(pi)/(4) - (1)/(2) cos^(-1)x^(2)`

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

int(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(2))sqrt(1+x^(2)))dx=

The differential coefficient of tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))

lim_(x rarr0)(sqrt(1-x)-sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1+x))

The derivative of tan^(-1)((sqrt(1 + x)-sqrt(1-x))/(sqrt(1 + x)+sqrt(1-x))) is

If (sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))=3 then x=1)sqrt((2)/(3)2)sqrt((1)/(3))3)sqrt((2)/(5))sqrt((3)/(5))

tan^(-1)((sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))

Differentiate the following function (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1))

Differentiate (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)) with respect to x:

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1