153 |
tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) / |
tan(select(n a)) := (tan((n-1) select(a)) + tan(a)) / |
154 |
(1 - tan((n-1) a) tan(a)) |
(1 - tan((n-1) a) tan(a)) |
155 |
:: integer(n) :: n > 2, |
:: integer(n) :: n > 2, |
156 |
|
cot(select(a + b)) := (cot(select(a)) cot(b) - 1) / |
157 |
|
(cot(a) + cot(b)), |
158 |
sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b), |
sinh(select(a + b)) := sinh(select(a)) cosh(b) + cosh(a) sinh(b), |
159 |
cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b), |
cosh(select(a + b)) := cosh(select(a)) cosh(b) + sinh(a) sinh(b), |
160 |
tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) / |
tanh(select(a + b)) := (tanh(select(a)) + tanh(b)) / |
161 |
(1 + tanh(a) tanh(b)), |
(1 + tanh(a) tanh(b)), |
162 |
|
coth(select(a + b)) := (coth(select(a)) coth(b) + 1) / |
163 |
|
(coth(a) + coth(b)), |
164 |
x && select(a || b) := (x && select(a)) || (x && b), |
x && select(a || b) := (x && select(a)) || (x && b), |
165 |
select(a || b) && x := (select(a) && x) || (b && x), |
select(a || b) && x := (select(a) && x) || (b && x), |
166 |
! select(a && b) := (!a) || (!b), |
! select(a && b) := (!a) || (!b), |
273 |
sin(select(x)) := -sin(select(-x)), |
sin(select(x)) := -sin(select(-x)), |
274 |
cos(select(x)) := cos(select(-x)), |
cos(select(x)) := cos(select(-x)), |
275 |
tan(select(x)) := -tan(select(-x)), |
tan(select(x)) := -tan(select(-x)), |
276 |
|
sec(select(x)) := sec(select(-x)), |
277 |
|
csc(select(x)) := -csc(select(-x)), |
278 |
|
cot(select(x)) := -cot(select(-x)), |
279 |
arcsin(select(x)) := -arcsin(select(-x)), |
arcsin(select(x)) := -arcsin(select(-x)), |
280 |
arccos(select(x)) := 4 arctan(1) - arccos(select(-x)), |
arccos(select(x)) := 4 arctan(1) - arccos(select(-x)), |
281 |
arctan(select(x)) := -arctan(select(-x)), |
arctan(select(x)) := -arctan(select(-x)), |
282 |
sinh(select(x)) := -sinh(select(-x)), |
sinh(select(x)) := -sinh(select(-x)), |
283 |
cosh(select(x)) := cosh(select(-x)), |
cosh(select(x)) := cosh(select(-x)), |
284 |
tanh(select(x)) := -tanh(select(-x)), |
tanh(select(x)) := -tanh(select(-x)), |
285 |
|
sech(select(x)) := sech(select(-x)), |
286 |
|
csch(select(x)) := -csch(select(-x)), |
287 |
|
coth(select(x)) := -coth(select(-x)), |
288 |
arcsinh(select(x)) := -arcsinh(select(-x)), |
arcsinh(select(x)) := -arcsinh(select(-x)), |
289 |
arctanh(select(x)) := -arctanh(select(-x)), |
arctanh(select(x)) := -arctanh(select(-x)), |
290 |
select(x) = a := select(-x) = -a, |
select(x) = a := select(-x) = -a, |