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The trigonometric equation sin^(-1)x=2si...

The trigonometric equation `sin^(-1)x=2sin^(-1)a` has a solution for all real values

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`-pi/22<=sin^(-1)x<=pi/2`
`-pi/2<=2sina<=pi/2`
`-pi/4<=sina<=pi/4`
`-1/sqrt2<=a<=1/sqrt2`
`|a|<=1/sqrt2`.
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