Hi,

As far as I know, there is no simple way to verify such identities with Sage yet. A related issue is that Sage is currently unable to simplify `cosh(x) - (exp(x)+exp(-x))/2`

to `0`

:

```
sage: (cosh(x) - (exp(x)+exp(-x))/2).simplify_full()
1/2*(2*cosh(x)*e^x - e^(2*x) - 1)*e^(-x)
```

But there is a workaround: the `rewrite`

extension written by François Maltey. To use it, download the file `rewrite-20110123.sage`

from this page; then in a Sage session, you may ask to rewrite the hyperbolic functions in terms of exp, so that the outcome of the check is now `True`

:

```
sage: %runfile rewrite-20110123.sage
sage: bool( rewrite(cosh(x), 'sinhcosh2exp') == (exp(x)+exp(-x))/2 )
True
```

Equivalently, you may also ask to rewrite the whole identity:

```
sage: bool( rewrite(cosh(x) == (exp(x)+exp(-x))/2, 'sinhcosh2exp') )
True
```

See here for the documentation of `rewrite`

.
Hopefully, it shall be included in main Sage some day.