How do I prove that tanh(arcsinhx) = x/((x^2 + 1)^1/2)
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Start with the basic definitions and identities. $\displaystyle tanh(x)= \frac{sinh(x)}{cosh(x)}$. sinh(arcsih(x))= x, of course. Convert cosh(x) to sinh(x) using the identity [tex]cosh^2(x)- sinh^2(x)= 1.
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