8cosП/65 cos2П/65 cos4П/65 cos8П/65 cos16П/65 cos32П/65

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8cosП/65 cos2П/65 cos4П/65 cos8П/65 cos16П/65 cos32П/65


Алгебра (49 баллов) | 121 просмотров
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Правильный ответ

(8sinπ/65*cosπ/65*cos2π/65*cos4π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=(4sin2π/65*cos4π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=
=(2sin4
π/65*cos4π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=
=(sin8
π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=
=(sin16
π/65*cos16π/65*cos32π/65)/(2*sinπ/65)=
=(sin32
π/65*cos32π/65)/(4*sinπ/65)=(sin64π/65)/(8*sinπ/65)=
=(sin(π-π/65)/(8*sinπ/65)=(sinπ/65)/(8*sinπ/65)=1/8

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