180
[C] Formules trigonométriques
Arctan x + Arctan
1
x
=
π
2
sgn x
Trigonométrie hyperbolique
sh x =
e x − e −x
2
ch x =
e x + e −x
2
ch(a + b) = ch a ch b + sh a sh b
sh(a + b) = sh a ch b + ch a sh b
ch(a − b) = ch a ch b − sh a sh b
sh(a − b) = sh a ch b − ch a sh b
th(a + b) =
th a + th b
1 + th a th b
th(a − b) =
th a + th b
1 − th a th b
ch 2a =



ch
2 a + sh
2 a
2 ch
2 a − 1
1 + 2 sh
2 a
sh 2a = 2 sh a ch a
ch
2 x − sh
2 x = 1
th 2a =
2 th a
1 + th
2 a
ch p + ch q = 2 cosh
p + q
2
ch
p − q
2
ch p − ch q = 2 sh
p + q
2
sh
p − q
2
sh p + sh q = 2 sh
p + q
2
ch
p − q
2
sh p − sh q = 2 cosh
p + q
2
sh
p − q
2