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If x lt 0, the prove that cos^(-1) ((1 +...

If `x lt 0`, the prove that `cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x`

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To prove that \[ \cos^{-1} \left( \frac{1 + x}{\sqrt{2(1 + x^2)}} \right) = \frac{\pi}{4} - \tan^{-1}(x) \] for \( x < 0 \), we can follow these steps: ...
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