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Prove that cos[Tan^(-1){sin(Cot^(-1)x)}]...

Prove that `cos[Tan^(-1){sin(Cot^(-1)x)}] = sqrt((x^(2)+1)/(x^(2)+2))`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((1+x^(2))/(2+x^(2)))`
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Knowledge Check

  • Assertion: sin(cot^(-1)(1/2))=tan(cos^(-1)x) then the value of x=(sqrt(5))/3 Reason R: cos(tan^(-1)(sin(cot^(-1)x)))=sqrt(((1+x^(2))/(2+x^(2))))

    A
    Both A and R are true and R is correct explanation of A
    B
    Both A and R are true and R is not correct explanation of A
    C
    A is true, R is false
    D
    A is false but R is true

  • sin[cot^(-1){cos(tan^(-1)x)}]=

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

  • tan^(-1)(x+sqrt(1+x^(2)))=

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

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    tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

    sin(Cot^(-1)(cos(Tan^(-1)x)))=

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

    cos[2Sin^(-1)sqrt((1-x)/2)]=

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