求求tan15°，tan105°的值
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解决时间 2021-03-30 03:39
- 提问者网友：酱爆肉
- 2021-03-29 04:53
求求tan15°，tan105°的值
最佳答案
- 五星知识达人网友：等灯
- 2021-03-29 05:39
cos30 °= √¯3/2
cos15 °= √¯[(1 + cos30° )/2]
sin15° = √¯[(1 - cos30° )/2]
tan15° = sin15° /cos15°
= √¯[(1 - cos30° )/(1 + cos30° )]
= √¯[(2 - √¯3)/(2 + √¯3)]
= (2 - √¯3)
tan105°
=tan(45°+60°)
=(tan45°+tan60°)/(1-tan45°tan60°)
=（1+√3）/(1-√3)
=-2-√3
cos15 °= √¯[(1 + cos30° )/2]
sin15° = √¯[(1 - cos30° )/2]
tan15° = sin15° /cos15°
= √¯[(1 - cos30° )/(1 + cos30° )]
= √¯[(2 - √¯3)/(2 + √¯3)]
= (2 - √¯3)
tan105°
=tan(45°+60°)
=(tan45°+tan60°)/(1-tan45°tan60°)
=（1+√3）/(1-√3)
=-2-√3
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