def test_TR11():
assert TR11(sin(2*x)) == 2*sin(x)*cos(x)
assert TR11(sin(4*x)) == 4*((-sin(x)**2 + cos(x)**2)*sin(x)*cos(x))
assert TR11(sin(4*x/3)) == \
4*((-sin(x/3)**2 + cos(x/3)**2)*sin(x/3)*cos(x/3))
assert TR11(cos(2*x)) == -sin(x)**2 + cos(x)**2
assert TR11(cos(4*x)) == \
(-sin(x)**2 + cos(x)**2)**2 - 4*sin(x)**2*cos(x)**2
assert TR11(cos(2)) == cos(2)
assert TR11(cos(3*pi/7), 2*pi/7) == -cos(2*pi/7)**2 + sin(2*pi/7)**2
assert TR11(cos(4), 2) == -sin(2)**2 + cos(2)**2
assert TR11(cos(6), 2) == cos(6)
assert TR11(sin(x)/cos(x/2), x/2) == 2*sin(x/2)
def test_TR11():
assert TR11(sin(2 * x)) == 2 * sin(x) * cos(x)
assert TR11(sin(4 * x)) == 4 * ((-sin(x)**2 + cos(x)**2) * sin(x) * cos(x))
assert TR11(sin(x*Rational(4, 3))) == \
4*((-sin(x/3)**2 + cos(x/3)**2)*sin(x/3)*cos(x/3))
assert TR11(cos(2 * x)) == -sin(x)**2 + cos(x)**2
assert TR11(cos(4*x)) == \
(-sin(x)**2 + cos(x)**2)**2 - 4*sin(x)**2*cos(x)**2
assert TR11(cos(2)) == cos(2)
assert TR11(cos(pi * Rational(3, 7)),
pi * Rational(2, 7)) == -cos(pi * Rational(2, 7))**2 + sin(
pi * Rational(2, 7))**2
assert TR11(cos(4), 2) == -sin(2)**2 + cos(2)**2
assert TR11(cos(6), 2) == cos(6)
assert TR11(sin(x) / cos(x / 2), x / 2) == 2 * sin(x / 2)