Unexpected result for cos(a)^2 + sin(a)^2, question about variables

[erentar]

I would expect the following expression to evaluate to 1 but it does not.

```

var("a",domain="real")

simplify(cos(a)^2 + sin(a)^2)

```

How can i define a variable in this fashion that will result in the code evaluating to 1?

[Maxime Bombar]

Hi,

you can use the "full_simplify" method for that:


```
sage: var("a", domain="real")
a
sage: b = cos(a)^2+sin(a)^2
sage: b.simplify()
cos(a)^2 + sin(a)^2
sage: b.full_simplify()
1
```

Best,

--
Maxime

[Emmanuel Charpentier]

Also :

sage: b.simplify_trig()
1

Using specific simplifications in a specific order is often the key to get interesting results that the brute-force simplify_full cannot. Such simplifications are :

sage: import re
sage: print(", ".join([v[0] for v in list(map(lambda u:re.findall(".*simplify.*", u), dir(x))) if len(v)>0]))
factorial_simplify, full_simplify, hypergeometric_simplify, log_simplify, rational_simplify, simplify, simplify_factorial, simplify_full, simplify_hypergeometric, simplify_log, simplify_rational, simplify_real, simplify_rectform, simplify_trig, trig_simplify

to which you should add canonicalize_radical (with caution ! See this for example), and the x._sympy_().simplify()._sage_() idiom, extremely interesting alternative to full_simplify.

HTH,

​

[erentar2002]

Thank you!

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