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Prove that:tan^(-1)sqrt(x)=1/2cos^(-1)((...

Prove that:`tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)), x in [0,1]`

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To prove that \( \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left(\frac{1-x}{1+x}\right) \) for \( x \in [0,1] \), we can follow these steps: ### Step 1: Start with the given equation We start with the equation we need to prove: \[ \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left(\frac{1-x}{1+x}\right) \] ...
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