Répondre :
Montrer que sinus10 sinus30 sinus50 sinus70 =1/16
réponse :
sin(10°)sin(30°)sin(50°)sin(70°)
=cos(80°)cos(60°)cos(40°)cos(20°)
=1/2*(cos(20°)*cos(40°)*cos(80°))
or sin(20°)*(cos(20°)*cos(40°)*cos(80°))
=1/2*sin(40°)cos(40°)cos(80°)
=1/4*sin(80°)*cos(80°)
=1/8*sin(160°)
=1/8sin(180°-160°)
=1/8sin(20°)
donc
(cos(20°)*cos(40°)*cos(80°))=1/8
donc
sin(10°)sin(30°)sin(50°)sin(70°)=1/2*1/8=1/16
réponse :
sin(10°)sin(30°)sin(50°)sin(70°)
=cos(80°)cos(60°)cos(40°)cos(20°)
=1/2*(cos(20°)*cos(40°)*cos(80°))
or sin(20°)*(cos(20°)*cos(40°)*cos(80°))
=1/2*sin(40°)cos(40°)cos(80°)
=1/4*sin(80°)*cos(80°)
=1/8*sin(160°)
=1/8sin(180°-160°)
=1/8sin(20°)
donc
(cos(20°)*cos(40°)*cos(80°))=1/8
donc
sin(10°)sin(30°)sin(50°)sin(70°)=1/2*1/8=1/16