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If 0 lt x lt 1", then " sqrt(1+x^(2))[...

If `0 lt x lt 1", then " sqrt(1+x^(2))[{x cos (cot^(-1)x) + sin ( cot^(-1) x)}^(2) -1]^(1//2) ` is equal to

A

`x/(sqrt1+x^(2))`

B

`x`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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If 0ltxlt1 then sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1]^(1/2)

Knowledge Check

  • If 0 lt x le 1, " then " sqrt(1+x^2) {x cos (cot^(-1)x)+sin(cot^(-1)x)}^(1//2)=

    A
    `x/(sqrt(1+x^2))`
    B
    x
    C
    `x sqrt(1+x^2)`
    D
    none of these

  • If 0lt xlt1, then sqrt(1+x^2)[{x cos (cot^-1x)+sin(cot^-1x)}^2-1]^(1//2) is equal to

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

  • If [ x cos ( cot^(-1) x ) + sin ( cot^(-1) x) ]^(2) = (51)/(50) then the positive value of x is

    A
    `(1)/(sqrt(2))`
    B
    `(1)/(5 sqrt(2))`
    C
    `2 sqrt(2)`
    D
    `5 sqrt(2)`

    • Similar Questions

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