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If sin^(-1)x=2sin^(-1)alpha has a soluti...

If `sin^(-1)x=2sin^(-1)alpha` has a solution, then

A

all real values

B

`|a| lt (1)/(2)`

C

`|a| le (1)/(sqrt2)`

D

`(1).(2) lt |a| lt (1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin^(-1) x = 2 sin^(-1) a`
Now `-(pi)/(2) le sin^(-1) a le(pi)/(2)`
`rArr -(pi)/(4) le sin^(-1) a le (pi)/(4)`
`rArr -(1)/(sqrt2) le a le (1)/(sqrt2)`
`rArr |a| le (1)/(sqrt2)`
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