exo33 p.373
cos (pi-x)+ cos (x-3pi)
=[cos pi cos(-x) + sin pi sin (-x)] + [ cos x cos (-3pi) + sin x sin (3pi)]
=[cos pi cos (x) - sin pi sin (x)] + [ cos x cos (3pi) -sin x sin (3pi)]
=-cos (x) - sin (x)+cos(x)
b) sin(-x)-sin(pi+x)=-sin(x)-sin(x)=-2sin(x)
c) sin(-x)-cos(-x)=-sin(x) -cos(x)
d) sin(pi+x)+cos(-x)=-sin(x)-cos(x)
e) cos(-pi-x)+sin(x-pi)+sin(4pi-x)=-cos(x)-sin(x)-sin(x)=-cos(x)-2sin(x)
exo 68 p 376
Application :
sin(x-pi/7) + sin (x+pi/7) = 2sin(x)cos(pi/7)
sin(x)=0 <=> x= 0 ou pi ou 2pi
exo 66 p.376
sin(pi/12 fois 2)
= 2sin(pi/12)cos(pi/12)
=2 (V6-V2)/4 (V6+V2)/4
=(6-2)/8
= 1/2
sin (pi/6)=1/2
cos(pi/12 fois 2)
= cos(pi/12)^2 - sin(pi/12)^2
= ( (V6+V2)/4) )^2 - ( (V6-V2)/4) )^2
= (6+4V3+2-6+4V3-2)/16 = V3/2
cos(pi/6)= V3/2