求cos1°+cos2°+cos3°+...+cos178°+cos179°的值(这里的数字都是度数比如1°)求cos1°+cos2°+cos3°+...+cos178°+cos179°的值

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求cos1°+cos2°+cos3°+...+cos178°+cos179°的值(这里的数字都是度数比如1°)求cos1°+cos2°+cos3°+...+cos178°+cos179°的值

求cos1°+cos2°+cos3°+...+cos178°+cos179°的值(这里的数字都是度数比如1°)求cos1°+cos2°+cos3°+...+cos178°+cos179°的值
求cos1°+cos2°+cos3°+...+cos178°+cos179°的值(这里的数字都是度数比如1°)
求cos1°+cos2°+cos3°+...+cos178°+cos179°的值

求cos1°+cos2°+cos3°+...+cos178°+cos179°的值(这里的数字都是度数比如1°)求cos1°+cos2°+cos3°+...+cos178°+cos179°的值
cos1°+cos2°+cos3°+...+cos178°+cos179°
=(cos1°+cos179°)+(cos2°+cos178°)+……+(cos89°+cos91°)+cos90°
=(cos1°-cos1°)+(cos2°-cos2°)+……+(cos89°-cos89°)+cos90°
=cos90°
=0

2cos1度 可以首相和末尾相加就像从1加到100一样

答案为0:
cosα+cosβ=2cos[(α+β)/2] cos[(α-β)/2]
cos1°+cos179°=cos90° cos89°=0
cos2°+cos178°=cos90° cos88°=0
cos3°+cos177°=cos90° cos87°=0
..........
cos89°+cos91°=cos90° cos1°=0
cos90°=0
故cos1°+cos2°+cos3°+...+cos178°+cos179°=0