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

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

`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`