Re: [中學] 100年師大附中
※ 引述《iamOrz (I am Orz)》之銘言：
: 9 k kπ
: 求 Σ(-1) * cos ---- = ?
: k=1 19
: 已爬文. 請賜教 謝謝
= - cos π/19 + cos 2π/19 - cos 3π/19 + cos 4π/19 - cos 5π/19
+ cos 6π/19 - cos 7π/19 + cos 8π/19 - cos 9π/19
= - cos π/19 - cos 17π/19 - cos 3π/19 - cos15π/19 - cos 5π/19
-13cos 6π/19 - cos 7π/19 - cos11π/19 - cos 9π/19
= - (cos π/19 + cos 2π/19 + .... + cos17π/19)
同乘 sin π/19 ，再使用積化和差
= - 1/sin π/19 (cosπ/19 *sin π/19 + cos 2π/19 *sin π/19 + ....
+ cos17π/19 *sin π/19)
= .......
= - 1/sin π/19 * 1/2 * (sin0 + sin 18π/19)
= - 1/2
--
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