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Express sin^(-1).(sqrtx)/(sqrt(x + a)) a...

Express `sin^(-1).(sqrtx)/(sqrt(x + a))` as a function of `tan^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
`tan^(-1) (sqrt((x)/(a)))`
Putting `x = a tan^(2) theta`
`:. Sin.^(-1) (sqrtx)/(sqrt(x + a) = sin^(-1) (sqrta sqrt(tan^(2)theta))/(sqrt(a tan^(2) theta + a))`
`= sin.^(-1) (sqrta tan theta)/(sqrta sec theta)`
`= sin^(-1) sin theta = theta = tan^(-1) (sqrt((x)/(a)))`
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Knowledge Check

  • If f(x)=x(sqrtx+sqrt(x+1)) , then

    A
    f(x) is continuous but not differentiable at x=0
    B
    f(x) is differentiable at x=0
    C
    f(x) is not differentiable at x=0
    D
    None of the above

  • If y=sec^(-1)""(sqrtx+1)/(sqrtx-1)+sin^(-1)""(sqrtx-1)/(sqrtx+1) , then (dy)/(dx) is equal to

    A
    0
    B
    `(1)/(sqrtx+1)`
    C
    1
    D
    3

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