Inverse Hyperbolic Cosine of x [cosh^{-1}=ln (x+\sqrt{x^{1}-1})]

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This video describes how to prove the identity cosh^{-1}x=ln(x+\sqrt{x^{2}-1}) analytically.
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The beauty is in the neatness of this presentation plus the gentleness of the voice.

PrimeNewtons
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I dont quite undestand the last part that how can we sure negative sign is reducdent.

xeletna