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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]`

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To prove that \( 3 \cos^{-1} x = \cos^{-1}(4x^3 - 3x) \) for \( x \in \left[\frac{1}{2}, 1\right] \), we can follow these steps: ### Step 1: Let \( x = \cos \theta \) We start by letting \( x = \cos \theta \). This implies that \( \theta = \cos^{-1} x \). ### Step 2: Express \( 3 \cos^{-1} x \) in terms of \( \theta \) Using our substitution, we rewrite the left-hand side: \[ ...
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