sinh(x) and cosh(x)

**Alexrey** · June 13th 2011, 06:35 AM

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

**Prove It** · June 13th 2011, 06:37 AM

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

**Alexrey** · June 13th 2011, 08:37 AM

Thanks very much PI.

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