Solve `sin^(-1)(1-x)-2sin^(-1)x=pi/2`

1.	Solve `sin^(-1)(1-x)-2sin^(-1)x=pi/2`
Answer» `sin^(-1)(1-x)-2sin^(-1)x=pi/2` Let `x=siny` `sin^(-1)(1-siny)=2y=pi/2` `sin^(-1)(1-siny)=(pi/2+2y)` `1-siny=cos2y` `1-siny=1-2sin2y` `2sin^2y=siny` `siny=0,siny=1/2` `siny=0,x=0` `sin=1/2,x=1/2` `sin^(-1)1=pi/2` `sin^(-1)1/22-2sin^(-1)1/2` `-sin^(-1)1/2` `-x/6!=pi/2`.

Discussion

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