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sin(cos^(-1)x)=...

`sin(cos^(-1)x)=`

A

`sqrt(1+x^(2))`

B

x

C

`(1+x^(2))^(-3//2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • If y=(sin^(-1)x-cos^(-1)x)/(sin^(-1)x+cos^(-1)x)," then "(dy)/(dx)=

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

  • The value of x satisfying the equation (sin^(-1)x)^3 - (cos^(-1)x)^3 + (sin^(-1)x) (cos^(-1)x)(sin^(-1)x - cos^(-1)x) = (pi^3)/(16) is

    A
    `"cos" pi/5`
    B
    `"cos" pi/4`
    C
    `"cos" pi/8`
    D
    `"cos" pi/12`

  • The value of x satisfying the equation (sin^(-1)x)^(3)-(cos^(-1)x)^(3)+(sin^(-1)x)(cos^(-1)x)(sin^(-1)x-cos^(-1)x)=(pi^(3))/(16) is :

    A
    `"cos"(pi)/(5)`
    B
    `"cos"(pi)/(4)`
    C
    `"cos"(pi)/(8)`
    D
    `"cos"(pi)/(12)`

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