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3sin^-1x=sin(3x-4x^3), x in [-1/2,1/2]...

`3sin^-1x=sin(3x-4x^3), x in [-1/2,1/2] `

Text Solution

Verified by Experts

Let `x = siny`
Then,
`L.H.S. = 3sin^-1x = 3sin^-1(sin y) = 3y`
`R.H.S. = sin^-1(3x-4x^3) = sin^-1(3siny-4sin^3y)`
`=sin^-1(sin3y) = 3y`
Hence, `L.H.S. = R.H.S.`
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