化简sin π/7(cos2π/7+cos4π/7+cos6π/7)

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化简sin π/7(cos2π/7+cos4π/7+cos6π/7)
化简sin π/7(cos2π/7+cos4π/7+cos6π/7)

化简sin π/7(cos2π/7+cos4π/7+cos6π/7)
根据积化和差公式,得
原式
=sinπ/7cos2π/7+sinπ/7cos4π/7+sinπ/7cos6π/7
=cos2π/7sinπ/7+cos4π/7sinπ/7+cos6π/7sinπ/7
=(sin3π/7-sinπ/7)/2+(sin5π/7-sin3π/7)/2+(sinπ-sin5π/7)/2
=(sin3π/7-sinπ/7+sin5π/7-sin3π/7+sinπ-sin5π/7)/2
=(sinπ-sinπ/7)/2
=(0-sinπ/7)/2
=-(sinπ/7) /2




所用公式: