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

`tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))),absxx le 1/sqrt2`, is equal to

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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If tan^(-1) (sqrt(1+x^2)-sqrt(1-x^2))/(sqrt((1+x^2))+sqrt((1-x^2))

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Knowledge Check

  • The value of tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))],|x|lt1/2 x is !=0 equal to

    A
    `(pi)/4+1/2"cos^(-1)x^(2)`
    B
    `(pi)/4-"cos"^(-1)x^(2)`
    C
    `(pi)/4-1/2cos^(-1)x^(2)`
    D
    `(pi)/4+cos^(-1)x^(2)`

  • If y=tan^(-1)""(sqrt(1+x^2)-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) , then (dy)/(dx) is equal to

    A
    `(x^(2))/(sqrt(1-x^(4)))`
    B
    `(x^(2))/(sqrt(1-x^(4)))`
    C
    `(x)/(sqrt(1+x^(4)))`
    D
    `(x)/(sqrt(1-x^(4)))`

  • If y= tan^(-1) ""[(sqrt(1+x^2)+ sqrt(1-x^2))/( sqrt(1+x^2)- sqrt(1-x^2))], then (dy)/(dx) equals

    A
    `(1)/(sqrt(1-x^4))`
    B
    `-(1)/( sqrt(1-x^4))`
    C
    `(x)/( sqrt(1-x^4))`
    D
    `-(x)/(sqrt(1-x^4))`

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    If y=tan^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))), x^2 le 1 , then find (dy)/(dx)

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    if tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=alpha then

    if tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))}=alpha then

    y=(tan^(-1)(sqrt(1+x^(2))+sqrt(1-x^(2))))/(sqrt(1+x^(2))-sqrt(1-x^(2))) then (dy)/(dx)

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