Ответы на вопрос:
Sin(α+β) +sin(α-β) =2sinα*cosβ⇔ sinα*cosβ = (1/2)* (sin(α+β) +sin(α-β) ). cos2π/7 +cos4π/7+ cos6π/7 =2sinπ/7*(cos2π/7 +cos4π/7+ cos6π/7)/2sinπ/7= (2sinπ/7*cos2π/7 +2sinπ/7*cos4π/7+ 2sinπ/7*cos6π/7)/2sinπ/7= (sin3π/7 -sinπ/7 +sin5π/7-sin3π/7+sinπ -sin5π/7) / 2sinπ/7 = -(sinπ/7) / 2sinπ/7 = -1/2.
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