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f(x)=sin{cot^(-1)(x+1)}-cos(tan^(-1)x), ...

`f(x)=sin{cot^(-1)(x+1)}-cos(tan^(-1)x),
The value of x for which f(x) = 0 is

A

`-1//2`

B

0

C

`1//2`

D

1

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • 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))`

  • sin(Cot^(-1)(cos(Tan^(-1)x)))=

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

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    A
    `1//2`
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    `2//3`
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    D
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