Buna ziua

Sa se calculeze expresia:

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Daca se noteaza suma cu S, atunci 

S = cos(2π/7) + cos(4π/7) + cos(6π/7). Se inmulteste suma cu sin(π/7) =>

2S*sin(π/7) = 2sin(π/7)*cos(2π/7) + 2sin(π/7)*cos(4π/7) + 2sin(π/7)*cos(6π/7) = 

= sin(3π/7) - sin(π/7) + sin(5π/7) - sin(3π/7) + sin(7πpi/7) - sin(5π/7)  = sinπ - sin(π/7) = -sin(π/7).

Se obtine 2S*sin(π/7) = -sin(π/7).

Simplificand cu -2sin(π/7), se poate scrie S = -1/2.

Am folosit formulele: sina*cosb = (1/2)*[sin(a+b) + sin(a-b)] si sin(-x) = -sinx (si faptul ca sinπ = 0).

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