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If sin^(-1)(1-x) sin^(-1)x=(pi)/(2) then...

If `sin^(-1)(1-x) sin^(-1)x=(pi)/(2)` then x equal

A

`0,-(1)/(2)`

B

`0,(1)/(2)`

C

0

D

3,4

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `sin^(-1)(1-x)=(pi)/(2)+2sin^(-1)x`
`rArr1-x=sin((pi)/(2)+2sin^(-1)x)`
`rArr1-x=cos(2sin^(-1)x)`
`rArr1-x=cos(2cos^(-1)sqrt(1-x^(2)))`
`rArr1-x=cos[cos^(-1)(2sqrt(1-x^(2)))^(2)-1]`
`rArr1-x=cos{cos^(-1)(1-2x^(2))}`
`rArr1-x=1-2x^(2)rArr2x^(2)-x=0`
`rArrx=0,(1)/(2)`
`thereforex=0[becausex=(1)/(2)` does not satisfy the given equation]
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