1.

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

Answer»

Solution :Put `sin^(-1) x = y`. Then sin y = x
`therefore 3 x - 4 x^3 = 3 sin y - 4 sin^3 y = sin 3Y`
`implies 3y = sin^(-1) (3X - 4x^3)`
`implies 3 sin^(-1) x = sin^(-1) (3x - 4x^3)`


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