Find value of $\cos h (2 x) + \sin h (2 x)$

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Solution

We know that,
$\cos h (2 x) = \frac{e^{2 x} + e^{- 2 x}}{2}$
$\sin h (2 x) = \frac{e^{2 x} - e^{- 2 x}}{2}$
therefore,
$\cos h (2 x) + \sin h (2 x)$
$= \frac{e^{2 x} + e^{- 2 x}}{2} + \frac{e^{2 x} - e^{- 2 x}}{2} = \frac{e^{2 x} + e^{- 2 x} + e^{2 x} - e^{- 2 x}}{2} = \frac{2 e^{2 x}}{2} = e^{2 x}$
Hence, value of $\cos h (2 x) + \sin h (2 x)$ is $e^{2 x}$

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