# How to simplify 1-cos(u)^2.

I have tried

```
sage: assume(0<u<pi/2)
```

But I still get

```
sage: simplify(1-cos(u)^2)
-cos(u)^2 + 1
```

How to simplify 1-cos(u)^2.

I have tried

```
sage: assume(0<u<pi/2)
```

But I still get

```
sage: simplify(1-cos(u)^2)
-cos(u)^2 + 1
```

add a comment

3

There are far more simplify methods. `expr.simplify?`

gives a hint:

See also: "simplify_full()", "simplify_trig()", "simplify_rational()", "simplify_rectform()", "simplify_factorial()", "simplify_log()", "simplify_real()", "simplify_hypergeometric()", "canonicalize_radical()"

In this case `simplify_trig`

will do the job.

```
var('u')
expr = 1-cos(u)^2
expr.simplify_trig()
```

2

Note that sometimes the "degree reduction" (of the involved trigonometric polynomial) is the wanted and/or needed "simplification".

The corresponding method is called `reduce_trig`

.

The following sample code shows some differences.

```
sage: var('u');
sage: a = 1 - cos(u)^2
sage: a.simplify_trig()
sin(u)^2
sage: a.reduce_trig()
-1/2*cos(2*u) + 1/2
sage: a.simplify_trig().reduce_trig()
-1/2*cos(2*u) + 1/2
sage: a.reduce_trig().simplify_trig()
sin(u)^2
```

With an other example...

```
sage: b = sin(u)^4 - cos(u)^4
sage: b.simplify_trig()
-2*cos(u)^2 + 1
sage: b.reduce_trig()
-cos(2*u)
```

1

`sympy`

. See http://docs.sympy.org/latest/tutorial/simplification.html for some simplification options.

Asked: **
2017-06-21 02:36:32 -0500
**

Seen: **242 times**

Last updated: **Jun 21 '17**

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