Updates:
Status: Valid
Labels: -Priority-Low Priority-Medium Simplify
Comment #1 on issue 3896 by [email protected]: sum of three-phase cos^2 or
cos^4 do not simplify to 3/2 and 9/8, respectively
http://code.google.com/p/sympy/issues/detail?id=3896
The k = 2 case works in master:
In [22]: k = 2
In [23]: simplify(cos(theta)**k + cos(theta+2*pi/3)**k +
cos(theta+4*pi/3)**k)
Out[23]: 3/2
k = 4 does not, though. trigsimp implements the algorithm from "Automated
and readable simplification of trigonometric expressions" by Fu, et. al.
It is possible to do this simplification in any case, though. Just
explicitly call expand_trig on it first. This will expand the sines and
cosines using the sum formulas, and the rest is just simplification using
sin(theta)**2 + cos(theta)**2 = 1, which trigsimp is quite good at.
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