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Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3)...

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

Text Solution

Verified by Experts

Let `sin^(-1)x=theta`
` implies x =sin theta`
RHS`=sin^(-1)(3x-4x^(3))`
`=sin^(-1)(sin3theta)`
`= 3 theta`
`= 3 sin^(-1)x`= LHS. Hence Proved.
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