We start by substituting the definitions of cosh x and sinh x:
cosh x + sinh x = (e^x + e^(-x))/2 + (e^x - e^(-x))/2.
Combining the fractions, we get:
cosh x + sinh x = (e^x + e^(-x) + e^x - e^(-x))/2.
Simplifying the numerator, we have:
cosh x + sinh x = (2e^x)/2.
Simplifying the rational expression, we get:
cosh x + sinh x = e^x.
Verify the following using the definitions of the hyperbolic functions.
csh x + sinh x = e^x
First, substitute the definitions of cosh x and sinh x. choose the correct substitution.
Then combine the fractions in the result above and simplify the numerator.
Then, simplify the rational expression above.
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