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Find cot^(-1) ( sqrt((1-x^(2))/(1 + x^(2...

Find `cot^(-1) ( sqrt((1-x^(2))/(1 + x^(2))))` in terms of cos

A

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

B

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

C

`pi/3 - 1/2 cos^(-1) ( x^(2))`

D

None of these

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • intcos(2cot^(-1)sqrt((1-x)/(1+x)))dx=

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

  • (d)/(dx)[cot^-1((1+sqrt(1-x^(2)))/(x))]=

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

  • If I = int_0^1 "cos" (2 "cot"^(-1) sqrt((1 - x)/(1 + x))) dx , then

    A
    `I gt 1/2`
    B
    `I = - 1/2`
    C
    `0 lt I lt 1/2`
    D
    none of these

    • Similar Questions

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    int_(0)^(1)cos(2cot^(-1)(sqrt((1-x)/(1+x)))

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    Prove the following: cos{tan^(-1){sin(cot^(-1)x)}}=sqrt((1+x^(2))/(2+x^(2)))

    int cos[2cot^(-1)sqrt((a-x)/(a+x))]dx

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