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The number of solution (s) of the equati...

The number of solution `(s)` of the equation `sin^(- 1)(1-x)-2sin^(- 1)x=pi/2` is/are

A

`0, 1/2`

B

`1, 1/2`

C

`0`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin^(-1)(1-x)+2sin^(-1)x=(pi)/(2)`
`rArr sin^(-1)(1-x)=((pi)/(2)-2sin^(-1)x)`
`rArr 1-x =sin((pi)/(2)-2 sin^(-1)x)`
`rArr 1-x sin.(pi)/(2)cos(2 sin^(-1)x)-cos.(pi)/(2)sin(2sin^(-1)x)`
`rArr 1-x cos (2sin^(-1)x)^(2)`
`rArr 1-x=cos(cos^(-1)(1-2x^(2)))rArr 2x^(2)-x=0`
`rArr x =0` or `x = 1//2`
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