Réponses

  • Utilisateur Brainly
2013-08-08T21:26:59+02:00

sin3x/sinx + cos3x/ cosx

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

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

=(2sin(x)cos²(x)+sin(x)cos(2x))/sin(x)+(cos(2x)cos(x)-2sin²(x)cos(x))/cos(x)

=2cos²(x)+cos(2x)+cos(2x)-2sin²(x)

=1+cos(2x)+2cos(2x)-1+cos(2x)

=4cos(2x)