Mathc initiation/a566

Un livre de Wikilivres.

Sommaire


Transformer des produits en sommes :
* Trigonométrie * Trigonométrie hyperbolique
cos(x)**2 = 1/2 + 1/2 cos(2x)
sin(x)**2 = 1/2 - 1/2 cos(2x)

cos(x)**3 =       3/4 cos(x)  + 1/4 cos(3x)
sin(x)**3 =       3/4 sin(x)  - 1/4 sin(3x)

cos(x)**4 = 3/8 + 1/2 cos(2x) + 1/8 cos(4x)
sin(x)**4 = 3/8 - 1/2 cos(2x) + 1/8 cos(4x)

cos(x) sin(x)  =  sin(2x)/2

sin(x)sin(y) = 1/2 [cos(x-y) - cos(x+y)]
cos(x)cos(y) = 1/2 [cos(x-y) + cos(x+y)]

sin(x)cos(y) = 1/2 [sin(x-y) + sin(x+y)]
cosh(x)**2 = 1/2 + 1/2 cosh(2x)
sinh(x)**2 = 1/2 cosh(2x) - 1/2

cosh(x)**3 = 3/4 cosh(x) + 1/4 cosh(3x)
sinh(x)**3 = 1/4 sinh(3x) - 3/4 sinh(x)

cosh(x)**4 = 3/8 + 1/2 cosh(2x) + 1/8 cosh(4x)
sinh(x)**4 = 3/8 - 1/2 cosh(2x) + 1/8 cosh(4x)

cosh(x) sinh(x) = sinh(2x)/2 

sinh(x) sinh(y) = 1/2 [cosh(x+y) - cosh(x-y)]
cosh(x) cosh(y) = 1/2 [cosh(x-y) + cosh(x+y)]

sinh(x) cosh(y) = 1/2 [sinh(x-y) + sinh(x+y)]