Am I correct in saying that sinh(x) = 0 only when x = 0 and cosh(x) never equals 0?

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- Jun 13th 2011, 06:35 AMAlexreysinh(x) and cosh(x)
Am I correct in saying that sinh(x) = 0 only when x = 0 and cosh(x) never equals 0?

- Jun 13th 2011, 06:37 AMProve It
Yes. To prove it, write $\displaystyle \displaystyle \sinh{x} = \frac{e^x - e^{-x}}{2}$, set it equal to 0 and solve for $\displaystyle \displaystyle x$. Also, set $\displaystyle \displaystyle \cosh{x} = \frac{e^x + e^{-x}}{2}$, and show that this is always positive.

- Jun 13th 2011, 08:37 AMAlexrey
Thanks very much PI.