Merge 2011e3a into 3cdc368

sympy/functions/elementary/tests/test_trigonometric.py

@@ -2,7 +2,7 @@
         acos, Rational, sqrt, asin, acot, coth, E, S, tan, tanh, cos,
         cosh, atan2, exp, log, asinh, acoth, atanh, O, cancel, Matrix, re, im,
         Float, Pow, gcd, sec, csc, cot, diff, simplify, Heaviside, arg,
-        conjugate, series, FiniteSet, asec, acsc)
+        conjugate, series, FiniteSet, asec, acsc, sech, csch)
 from sympy.core.compatibility import range
 from sympy.utilities.pytest import XFAIL, slow, raises
 
@@ -531,15 +531,15 @@ def test_cot():
     assert cot(7*pi/6) == sqrt(3)
     assert cot(-5*pi/6) == sqrt(3)
 
-    assert cot(pi/8).expand() == 1 + sqrt(2)
-    assert cot(3*pi/8).expand() == -1 + sqrt(2)
-    assert cot(5*pi/8).expand() == 1 - sqrt(2)
-    assert cot(7*pi/8).expand() == -1 - sqrt(2)
+    assert cot(pi/8).simplify() == 1 + sqrt(2)
+    assert cot(3*pi/8).simplify() == -1 + sqrt(2)
+    assert cot(5*pi/8).simplify() == 1 - sqrt(2)
+    assert cot(7*pi/8).simplify() == -1 - sqrt(2)
 
-    assert cot(pi/12) == sqrt(3) + 2
-    assert cot(5*pi/12) == -sqrt(3) + 2
-    assert cot(7*pi/12) == sqrt(3) - 2
-    assert cot(11*pi/12) == -sqrt(3) - 2
+    assert cot(pi/12).simplify() == sqrt(3) + 2
+    assert cot(5*pi/12).simplify() == -sqrt(3) + 2
+    assert cot(7*pi/12).simplify() == sqrt(3) - 2
+    assert cot(11*pi/12).simplify() == -sqrt(3) - 2
 
     assert cot(pi/24).radsimp() == sqrt(2) + sqrt(3) + 2 + sqrt(6)
     assert cot(5*pi/24).radsimp() == -sqrt(2) - sqrt(3) + 2 + sqrt(6)
@@ -569,7 +569,7 @@ def test_cot():
 
     assert cot(x).is_finite is None
     assert cot(r).is_finite is None
-    i = Symbol('i', imaginary=True)
+    i = Symbol('i', imaginary=True, nonzero=True)
     assert cot(i).is_finite is True
 
     assert cot(x).subs(x, 3*pi) == zoo
@@ -1158,8 +1158,8 @@ def test_sec():
     assert sec(5*pi/2) == zoo
     assert sec(9*pi/7) == -sec(2*pi/7)
     assert sec(3*pi/4) == -sqrt(2)  # issue 8421
-    assert sec(I) == 1/cosh(1)
-    assert sec(x*I) == 1/cosh(x)
+    assert sec(I) == sech(1)
+    assert sec(x*I) == sech(x)
     assert sec(-x) == sec(x)
 
     assert sec(asec(x)) == x
@@ -1235,8 +1235,8 @@ def test_csc():
     assert csc(5*pi/2) == 1
     assert csc(9*pi/7) == -csc(2*pi/7)
     assert csc(3*pi/4) == sqrt(2)  # issue 8421
-    assert csc(I) == -I/sinh(1)
-    assert csc(x*I) == -I/sinh(x)
+    assert csc(I) == -I*csch(1)
+    assert csc(x*I) == -I*csch(x)
     assert csc(-x) == -csc(x)
 
     assert csc(acsc(x)) == x