How do you prove $sinhx +coshx=e^x$ ?

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Answer 1 · 2016-05-04T14:54:32

see below

Use the definition $cosh x = (e^x+e^-x)/2 and sinh x = (e^x-e^-x)/2$

Left Side: $=cosh x + sinh x$

$=(e^x+e^-x)/2 +(e^x-e^-x)/2$

$=(e^x+e^-x +e^x-e^-x)/2$

$=(e^x +e^x)/2$

$=(2e^x)/2$

$=e^x$

How do you prove sinhx +coshx=e^xsinhx +coshx=e^x?