tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) /
(1 - tan((n-1) a) tan(a))
:: integer(n) :: n > 2,
+cot(select(a + b)) := (cot(select(a)) cot(b) - 1) /
+ (cot(a) + cot(b)),
sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b),
cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b),
tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) /
(1 + tanh(a) tanh(b)),
+coth(select(a + b)) := (coth(select(a)) coth(b) + 1) /
+ (coth(a) + coth(b)),
x && select(a || b) := (x && select(a)) || (x && b),
select(a || b) && x := (select(a) && x) || (b && x),
! select(a && b) := (!a) || (!b),
sin(select(x)) := -sin(select(-x)),
cos(select(x)) := cos(select(-x)),
tan(select(x)) := -tan(select(-x)),
+sec(select(x)) := sec(select(-x)),
+csc(select(x)) := -csc(select(-x)),
+cot(select(x)) := -cot(select(-x)),
arcsin(select(x)) := -arcsin(select(-x)),
arccos(select(x)) := 4 arctan(1) - arccos(select(-x)),
arctan(select(x)) := -arctan(select(-x)),
sinh(select(x)) := -sinh(select(-x)),
cosh(select(x)) := cosh(select(-x)),
tanh(select(x)) := -tanh(select(-x)),
+sech(select(x)) := sech(select(-x)),
+csch(select(x)) := -csch(select(-x)),
+coth(select(x)) := -coth(select(-x)),
arcsinh(select(x)) := -arcsinh(select(-x)),
arctanh(select(x)) := -arctanh(select(-x)),
select(x) = a := select(-x) = -a,