Buktikan Cos A + Cos ( A + 2pi/3) + cos (A + 4pi/3) =0
Matematika
Yuniasrahma1
Pertanyaan
Buktikan Cos A + Cos ( A + 2pi/3) + cos (A + 4pi/3) =0
1 Jawaban
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1. Jawaban Anonyme
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