Comment #14 on issue 1562 by [email protected]: Have trigsimp apply factor
and Poly.cancel() to sin's and cos's
http://code.google.com/p/sympy/issues/detail?id=1562
Here are some test collected from some issues involving trigsimp:
eq = -4*sin(x)**4 + 4*cos(x)**4 - 8*cos(x)**2
assert trigsimp(eq) == -4
n = sin(x)**6 + 4*sin(x)**4*cos(x)**2 + 5*sin(x)**2*cos(x)**4 +
2*cos(x)**6
d = -sin(x)**2 - 2*cos(x)**2
assert trigsimp(eq) == -4
assert trigsimp(-2*cos(x)**2 + cos(x)**4 - sin(x)**4) == -1
f = Function('f')
C1, C2, C3, C4, C5 = symbols('C1:6')
assert dsolve(f(x).diff(x, 5) + 2*f(x).diff(x, 3) + f(x).diff(x) - 1,
f(x),
'nth_linear_constant_coeff_variation_of_parameters') == \
Eq(f(x), C1 + x + (C2 + C3*x - sin(x)**3/4)*cos(x) +
(C4 + C5*x + cos(x)**3/4)*sin(x) - sin(2*x)*cos(2*x)/8)
assert trigsimp(sin(x)**3+cos(x)**2*sin(x)) == sin(x)
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