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
I have tried
sage: assume(0<u<pi/2)
But I still get
sage: simplify(1-cos(u)^2)
-cos(u)^2 + 1
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()
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)
Just for completeness -- another option is to use sympy
. See http://docs.sympy.org/latest/tutorial/simplification.html for some simplification options.
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Asked: 2017-06-21 09:36:32 +0100
Seen: 518 times
Last updated: Jun 21 '17
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