Let
us now consider some trigonometric expressions. For example:

When you type this expression into Maxima, Maple or Mathematica, you must remember that is really a shorthand for . So let us try to obtain the above result in Maxima first:

The function

works on expressions such as and . In turn functiontrigsimpemploys the identities and to simplify expressions containing , , etc. to , , , . Further simplification, if needed, may be obtained by using functiontrigreduceon the result.^{2.4}

In Maple we don't have to muck around with specialised functions for
trigonometry. Maple has a general purpose wrapper called `simplify`,
which recognises the nature of the expression and applies appropriate rules
until the result is as compact and simple as possible:

Mathematica will do something quite different here with its own
version of `Simplify`:

We can use Maxima in order to check that

Function

gives a canonical simplified quasilinear form of a trigonometrical expression.^{2.5}

Mathematica also has similar functions, called `TrigExpand`,
`TrigFactor`, and `TrigReduce`, but its `TrigExpand`
doesn't work the same way as in Maxima: