Bonjour,
A = cos(2012 pi/2 + x) = cos(1006π+x) = cos(1006π)cos(x) - sin(1006π)sin(x)
(on a utilisé cos(a+b)=cos(a)cos(b)-sin(a)sin(b))
= 1*cos(x) - 0*sin(x) = cos(x).
B = sin(2013 pi/2 + x) = sin(2013 pi/2)cos(x) + cos(2013 pi/2)sin(x)
(on a utilisé sin(a+b)=sin(a)cos(b)+cos(a)sin(b))
= sin(2013 pi/2)*cos(x) + 0*sin(x) (car 2013 impair)
= sin(2013 pi/2)cos(x)
= sin(1006 pi + pi/2)cos(x) (car 2013 = 2*1006 + 1)
= [ sin(1006pi)cos(pi/2) + cos(1006pi)sin(pi/2) ] cos(x)
= (0+1)*cos(x)
= cos(x)
N'hésite pas si tu as des questions !