test_simplify.py 文件源码

def test_trigsimp1():
    x, y = symbols('x,y')

    assert trigsimp(1 - sin(x)**2) == cos(x)**2
    assert trigsimp(1 - cos(x)**2) == sin(x)**2
    assert trigsimp(sin(x)**2 + cos(x)**2) == 1
    assert trigsimp(1 + tan(x)**2) == 1/cos(x)**2
    assert trigsimp(1/cos(x)**2 - 1) == tan(x)**2
    assert trigsimp(1/cos(x)**2 - tan(x)**2) == 1
    assert trigsimp(1 + cot(x)**2) == 1/sin(x)**2
    assert trigsimp(1/sin(x)**2 - 1) == 1/tan(x)**2
    assert trigsimp(1/sin(x)**2 - cot(x)**2) == 1

    assert trigsimp(5*cos(x)**2 + 5*sin(x)**2) == 5
    assert trigsimp(5*cos(x/2)**2 + 2*sin(x/2)**2) == 3*cos(x)/2 + S(7)/2

    assert trigsimp(sin(x)/cos(x)) == tan(x)
    assert trigsimp(2*tan(x)*cos(x)) == 2*sin(x)
    assert trigsimp(cot(x)**3*sin(x)**3) == cos(x)**3
    assert trigsimp(y*tan(x)**2/sin(x)**2) == y/cos(x)**2
    assert trigsimp(cot(x)/cos(x)) == 1/sin(x)

    assert trigsimp(sin(x + y) + sin(x - y)) == 2*sin(x)*cos(y)
    assert trigsimp(sin(x + y) - sin(x - y)) == 2*sin(y)*cos(x)
    assert trigsimp(cos(x + y) + cos(x - y)) == 2*cos(x)*cos(y)
    assert trigsimp(cos(x + y) - cos(x - y)) == -2*sin(x)*sin(y)
    assert ratsimp(trigsimp(tan(x + y) - tan(x)/(1 - tan(x)*tan(y)))) == \
        sin(y)/(-sin(y)*tan(x) + cos(y))  # -tan(y)/(tan(x)*tan(y) - 1)

    assert trigsimp(sinh(x + y) + sinh(x - y)) == 2*sinh(x)*cosh(y)
    assert trigsimp(sinh(x + y) - sinh(x - y)) == 2*sinh(y)*cosh(x)
    assert trigsimp(cosh(x + y) + cosh(x - y)) == 2*cosh(x)*cosh(y)
    assert trigsimp(cosh(x + y) - cosh(x - y)) == 2*sinh(x)*sinh(y)
    assert ratsimp(trigsimp(tanh(x + y) - tanh(x)/(1 + tanh(x)*tanh(y)))) == \
        sinh(y)/(sinh(y)*tanh(x) + cosh(y))

    assert trigsimp(cos(0.12345)**2 + sin(0.12345)**2) == 1
    e = 2*sin(x)**2 + 2*cos(x)**2
    assert trigsimp(log(e)) == log(2)