values at which sinhx is zero

Here's the graph of the hyperbolic sine.........see for yourself where it = 0   ......

 

https://www.desmos.com/calculator/7scsgh5zne

 

$$\\sinh(x)=0\\\\
\frac{e^x-e^{-x)}}{2}=0\\\\\
e^x-e^{-x}=0\\
e^x=\frac{1}{e^x}\\
e^{2x}=1\\
2x=0\\
x=0$$

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