高中數學題

2012-05-19 12:29 am
根號3/cos290度+1/sin250度=?(請詳解)

回答 (2)

2012-05-19 1:54 am
✔ 最佳答案
(√3)/cos290° + 1/sin250°

= (√3)/cos(360°-70°) + 1/sin(180°+70°)

= (√3)/cos70° + 1/sin70°

= [(√3)sin70° + cos70°]/(sin70°cos70°)

= 4[(√3/2)sin70° + (1/2)cos70°]/(2sin70°cos70°)

= 4[sin70°cos30° + cos70°sin30°]/sin140°

= 4sin(70°-30°)/sin(180°-40°)

= 4sin40°/sin40°

= 4
參考: 賣女孩的火柴


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