Question

Se considera numerele reale a si b ,a+b=pi/3. Aratati ca 2 cos b = cos a + √3 sin a.

Answer 1

2cosb-cosa=rad3sina
cosb-2sin pi/6*sin((a-b)/2)=
cosb-2*1/2*sin((a-b)/2)=
cosb-sin((a-b)/2)=
sin(pi/2-b)-sin((a-b)/2)=2sin((pi/2-a)/2)*cos pi/6=2*sina*rad3/2=rad3sina