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

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

Text Solution

Verified by Experts

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