e^(2x) = sinh(2x) + cosh(2x) Verify the identity.

e^(2x)=sinh(2x)+cosh(2x)
Take note that hyperbolic sine and hyperbolic cosine are defined as

sinh(u) = (e^u-e^(-u))/2

cosh(u)=(e^u+e^(-u))/2
Apply these two formulas to express the right side in exponential form.
e^(2x)=(e^(2x)-e^(-2x))/2 + (e^(2x)+e^(-2x))/2
Adding the two fractions, the right side simplifies to
e^(2x) = (2e^(2x))/2
e^(2x)=e^(2x)
This proves that the given equation is an identity.
 
Therefore,  e^(2x)=sinh(2x)+cosh(2x)  is an identity.