def test_trigsimp_issues():
a, x, y = symbols('a x y')
# issue 4625 - factor_terms works, too
assert trigsimp(sin(x)**3 + cos(x)**2 * sin(x)) == sin(x)
# issue 5948
assert trigsimp(diff(integrate(cos(x)/sin(x)**3, x), x)) == \
cos(x)/sin(x)**3
assert trigsimp(diff(integrate(sin(x)/cos(x)**3, x), x)) == \
sin(x)/cos(x)**3
# check integer exponents
e = sin(x)**y / cos(x)**y
assert trigsimp(e) == e
assert trigsimp(e.subs(y, 2)) == tan(x)**2
assert trigsimp(e.subs(x, 1)) == tan(1)**y
# check for multiple patterns
assert (cos(x)**2/sin(x)**2*cos(y)**2/sin(y)**2).trigsimp() == \
1/tan(x)**2/tan(y)**2
assert trigsimp(cos(x)/sin(x)*cos(x+y)/sin(x+y)) == \
1/(tan(x)*tan(x + y))
eq = cos(2) * (cos(3) + 1)**2 / (cos(3) - 1)**2
assert trigsimp(eq) == eq.factor() # factor makes denom (-1 + cos(3))**2
assert trigsimp(cos(2)*(cos(3) + 1)**2*(cos(3) - 1)**2) == \
cos(2)*sin(3)**4
# issue 6789; this generates an expression that formerly caused
# trigsimp to hang
assert cot(x).equals(tan(x)) is False
# nan or the unchanged expression is ok, but not sin(1)
z = cos(x)**2 + sin(x)**2 - 1
z1 = tan(x)**2 - 1 / cot(x)**2
n = (1 + z1 / z)
assert trigsimp(sin(n)) != sin(1)
eq = x * (n - 1) - x * n
assert trigsimp(eq) is S.NaN
assert trigsimp(eq, recursive=True) is S.NaN
assert trigsimp(1).is_Integer
assert trigsimp(-sin(x)**4 - 2 * sin(x)**2 * cos(x)**2 - cos(x)**4) == -1
def test_trigsimp_issues():
a, x, y = symbols('a x y')
# issue 4625 - factor_terms works, too
assert trigsimp(sin(x)**3 + cos(x)**2*sin(x)) == sin(x)
# issue 5948
assert trigsimp(diff(integrate(cos(x)/sin(x)**3, x), x)) == \
cos(x)/sin(x)**3
assert trigsimp(diff(integrate(sin(x)/cos(x)**3, x), x)) == \
sin(x)/cos(x)**3
# check integer exponents
e = sin(x)**y/cos(x)**y
assert trigsimp(e) == e
assert trigsimp(e.subs(y, 2)) == tan(x)**2
assert trigsimp(e.subs(x, 1)) == tan(1)**y
# check for multiple patterns
assert (cos(x)**2/sin(x)**2*cos(y)**2/sin(y)**2).trigsimp() == \
1/tan(x)**2/tan(y)**2
assert trigsimp(cos(x)/sin(x)*cos(x+y)/sin(x+y)) == \
1/(tan(x)*tan(x + y))
eq = cos(2)*(cos(3) + 1)**2/(cos(3) - 1)**2
assert trigsimp(eq) == eq.factor() # factor makes denom (-1 + cos(3))**2
assert trigsimp(cos(2)*(cos(3) + 1)**2*(cos(3) - 1)**2) == \
cos(2)*sin(3)**4
# issue 6789; this generates an expression that formerly caused
# trigsimp to hang
assert cot(x).equals(tan(x)) is False
# nan or the unchanged expression is ok, but not sin(1)
z = cos(x)**2 + sin(x)**2 - 1
z1 = tan(x)**2 - 1/cot(x)**2
n = (1 + z1/z)
assert trigsimp(sin(n)) != sin(1)
eq = x*(n - 1) - x*n
assert trigsimp(eq) is S.NaN
assert trigsimp(eq, recursive=True) is S.NaN
assert trigsimp(1).is_Integer
assert trigsimp(-sin(x)**4 - 2*sin(x)**2*cos(x)**2 - cos(x)**4) == -1