How would you prove cosech^-1(x) = sinh^-1(-1/x)? Both cosech and sinh are meant to mean inverse. Thanks in advance.
Last edited by JQ2009; Jan 26th 2010 at 01:06 PM.
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Originally Posted by JQ2009 How would you prove cosech^-1(x) = sinh^-1(-1/x)? Both cosech and sinh are meant to mean inverse. Thanks in advance. let $\displaystyle \sinh^{-1} \frac 1x = y$. solve for $\displaystyle x$ and find the $\displaystyle \text{csch}^{-1} x$ from that Spoiler: $\displaystyle \sinh^{-1} \frac 1x = y$ $\displaystyle \Rightarrow \frac 1x = \sinh y$ $\displaystyle \Rightarrow x = \frac 1{\sinh y} = \text{csch } y$ $\displaystyle \Rightarrow \text{csch}^{-1} x = y = \sinh^{-1} \frac 1x$
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