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The solution set of inequality log(1/2) ...

The solution set of inequality `log_(1/2) sin^-1 x gt log_(1/2) cos^-1 x`

A

`x in [0, (pi)/(sqrt2)]`

B

`x in ((1)/(sqrt2), 1]`

C

`x in (0, (1)/(sqrt2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`"log"_(1//2) sin^(-1) x gt "log"_(1//2) cos^(-1) x`
`rArr cos^(-1) x gt sin^(-1) x, 0 lt x lt 1`
`rArr cos^(-1) x gt (pi)/(2) - cos^(-1) x, 0 lt x lt 1`
`rArr cos^(-1) x gt (pi)//(4), 0 lt x lt 1`
`rArr 0 lt x lt (1)/(sqrt2)`
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