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If "cosec" ^(-1) x = sin ^(-1) ((1)/(...

If `"cosec" ^(-1) x = sin ^(-1) ((1)/(x))` then x may be -

A

1

B

`-(1)/(2)`

C

`(3)/(2)`

D

`-(3)/(2)`

Text Solution

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The correct Answer is:
A, C, D
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Knowledge Check

  • If y="cosec"^(-1)((x+1)/(x-1))+cos^(-1)((x-1)/(x+1)) , then (dy)/(dx) is equal to -

    A
    1
    B
    `pi`
    C
    0
    D
    `(pi)/(2)`

  • If sec^(-1) x = "cosec" ^(-1) y , then the valuw of cos^(-1) ""(1)/(x) - sin ^(-1)""(1)/(y) will be

    A
    0
    B
    `(2 pi)/(3)`
    C
    `(5pi)/(6)`
    D
    `(pi)/(2)`

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    Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

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