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求cosπ/13+cos3π/13+cos5π/13+cos7π/13+cos9π/13+cos11π/14的值

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2 | 2012-12-15 23:33:12 | 显示全部楼层 |阅读模式

解答：这种题目利用积化和差公式裂项求和先求 2sin(π/13)*[cosπ/13+cos3π/13+cos5π/13+cos7π/13+cos9π/13+cos11π/13] (你的输入有点小错)
=[sin(2π/13)-sin(0)]+[sin(4π/13)-sin(2π/13)]+[sin(6π/13)-sin(4π/13)]+[sin(8π/13)-sin(6π/13)]
+[sin(10π/13)-sin(8π/13)]+[sin(12π/13)-sin(10π/13)] =sin(12π/13)-0 =sin(12π/13) =sin(π/13)∴ cosπ/13+c...

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