Nilai cos 2phi/7 + cos 4phi/7 + cos 6phi/7 = ...

Jawab :

cos 2π/7 + cos 4π/7 + cos 6π/7
Kalikan pembilang dan penyebut dg 2 sin π/7
= 1/(2 sin π/7) . [2 sin π/7 cos 2π/7 + 2 sin π/7 cos 4π/7 + 2 sin π/7 cos 6π/7]
= 1/(2 sin π/7) . [(sin 3π/7 - sin π/7) + (sin 5π/7 - 3π/7) + (sin 7π/7 - sin 5π/7)]
= 1/(2 sin π/7) . [ - sin π/7 + sin 7π/7 ]
= 1/(2 sin π/7) . (-sin π/7)
= -1/2