Question

Тригонометрия. Найти значение выражения!

$cos frac{2pi}{7} + cosfrac{4pi}{7} +cos frac{6pi}{7}$

Answer 1

sin(α+β) +sin(α-β) =2sinα*cosβ⇔
sinα*cosβ = (1/2)*(sin(α+β) +sin(α-β) ).
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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.