Add.Maths 大難題

sin5 + sin10 + sin15 + sin20 + ... + sin175
=sin5(sin5 + sin10 + sin15 + sin20 + ... + sin175)/sin5
=[(cos0-cos10)+(cos5-cos15)+(cos10-cos20)+...+(cos170-cos180)]/2sin5
=[(cos0+cos5+cos10+...+cos170)-(cos10+cos15+cos20+...+cos180)]/2sin5
=(cos0+cos5-cos175-cos180)/2sin5
=2(1+cos5)/2sin5
=(1+cos5)/sin5
=2cos^2(2.5) / 2sin(2.5)cos(2.5)
=cot(2.5)
=tan(87.5)

2007-02-27 22:53:25 補充：
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