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Question
Solve the following for x:
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
Solution
`sin^(-1)(1-x)-2sin^-1 x=pi/2`
`sin^(-1)(1-x)=pi/2+2sin^-1 x`
`=>(1-x)=sin(pi/2+sin^-1 x)`
`=>(1-x)=cos(2sin^-1 x)`
`=>(1-x)=cos(cos^-1 (1-2x^2))`
`=>(1-x)=(1-2x^2)`
`=>2x^2-x=0`
`=>x=0, x=1/2`
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