1)
=\frac{1}{2}(e^{-x} + e^x))
2)
=\frac{1}{2}(-e^{-x} + e^x))
cosh(x), sinh(x) and tanh(x) are known as "hyperbolic trigonometric purposes"
apart from being a model real life situations (such as hanging wire), they are also used to evaluate "imaginary hyperbolic angles" which have to do with the hyperbola
in order to evaluate things such as sin(x), cos(x) and tan(x) where x is imaginary, we developed the relations of sinh, cosh and tanh
they come from the relationship that cis(x) = e^(ix)
1) sinh(x) = -i sin(ix)
2) cosh(x) = cos(ix)
Hence, in order to evaluate things such as cos(i

)
We will say that cos(i

) = cosh(pi) =
)
So it becomes interesting that the cosine of an imaginary number is, in fact, a real number
That's essentially a little bit about the hyperbolic trigonometric functions