8cosп/65 cos2п/65 cos4п/65 cos8п/65 cos16п/65 cos32п/65

Question

Алгебра: 8cosп/65 cos2п/65 cos4п/65 cos8п/65 cos16п/65 cos32п/65

fraumiss93 · Answer

(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)=
=(2sin4π/65*cos4π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=
=(sin8π/65*cos8π/65*cos16π/65*cos32π/65)/(sinπ/65)=
=(sin16π/65*cos16π/65*cos32π/65)/(2*sinπ/65)=
=(sin32π/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

8cosп/65 cos2п/65 cos4п/65 cos8п/65 cos16п/65 cos32п/65

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