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The set of values of x satisfying |sin^(...

The set of values of `x` satisfying `|sin^(- 1)x|lt|cos^(- 1)x|,`is

A

`[-1,1//sqrt(2))`

B

`[-1,1//sqrt(2)]cup[1//sqrt(2),1]`

C

`(-1,1//sqrt(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `0le cos^(-1)xlepi`
`therefore |cos^(-1)x|=cos^(-1)x`

It is evident from the graphs of `y=|sin^(-1)x|and y=|cos^(-1)x|` that
`|sin^(-1)x|cos^(-1)x|for all x in [-1,1//sqrt(2)`
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