Prove the following identities.
$sin h (- x) = - sin h x$

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Solution

We know that;
$c o s h x = \frac{e^{x} + e^{- x}}{2}$

$s i n h x = \frac{e^{x} - e^{- x}}{2}$
Thus;
$s i n h (- x) = \frac{e^{- x} - e^{x}}{2}$

$\to s i n h (- x) = - (\frac{e^{x} - e^{- x}}{2})$
Hence;
$s i n h (- x) = - s i n h x$

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