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## Re: [Axiom-developer] unexpected behaviour of normalize(1-(cos(x))^2)

 From: Tim Daly Subject: Re: [Axiom-developer] unexpected behaviour of normalize(1-(cos(x))^2) Date: Wed, 05 Aug 2009 09:59:59 -0400 User-agent: Thunderbird 2.0.0.21 (Windows/20090302)

```Michael,

Trig identity substitutions are somewhat problematic in Axiom.
See the src/input/schaum* files for examples.

If the subexpression (1-cos(x)^2) occurs in your expression E you can write:

sinrule:=rule((1-cos(x)^2) == sin(x)^2)

and then use this rule for your expression E thus

sinrule(E)

Axiom will not derive several of the trig identities from scratch.

In your expression we have something of the form
(4a^2) / (a^2 + 1)^2    where a = tan(x/2)
so Axiom needs to show that
(a^2+1)^2 != 0
(a^2+1) != 0
a^2 != -1
a != i
or, by back-substitution
tan(x/2) != i
which it does not conclude automatically, even though this
is clearly true in the domain Expression(Integer).

Michael Becker wrote:
```
```    Hi,

Is this (30)  the expected bevaviour of 'normalize' ??

(29) -> normalize ((sin(x))^2+(cos(x))^2)
(29) ->
(29)  1
Type: Expression Integer

(30) -> normalize (1-(cos(x))^2)
(30) ->
x 2
4tan(-)
2
(30)  ----------------------
x 4        x 2
tan(-)  + 2tan(-)  + 1
2          2
Type: Expression Integer

```
-- Michael
```

```