Buktikan Cos A + Cos ( A + 2pi/3) + cos (A + 4pi/3) =0

jawab
2pi/3 = 2 (180)/3 = 120°
4pi/3 =  4(180)/3 = 240°
cos A + cos (A + 120 )  + cos (A +240) =
cos A + { 2 cos 1/2( A+120 + A +240) cos 1/2 (A+120 - A- 240)} =
= cos A +  2 cos 1/2 (2A+360) cos 1/2  (-120)}
= cos A  + 2 { cos (A+180)  cos (-60)}
= cos A + 2 { - cos A  (1/2) }
= cos A  - cos A
= 0