设α为锐角，若cos(α+π/6)=3/5，则sin(α-π/12)=
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解决时间 2021-02-08 05:03
- 提问者网友：我一贱你就笑
- 2021-02-08 00:43
设α为锐角，若cos(α+π/6)=3/5，则sin(α-π/12)=
最佳答案
- 五星知识达人网友：轻熟杀无赦
- 2021-02-08 01:37
cos(a+π/6)=3/5
sin(a+π/6)=4/5
sin(a-π/12)=sin[(a+π/6)-π/4]=sin(a+π/6)*cos(π/4)-cos(a+π/6)*sin(π/4)
=(4/5)*(√2/2)-(3/5)*(√2/2) =√2/10
sin(a+π/6)=4/5
sin(a-π/12)=sin[(a+π/6)-π/4]=sin(a+π/6)*cos(π/4)-cos(a+π/6)*sin(π/4)
=(4/5)*(√2/2)-(3/5)*(√2/2) =√2/10
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- 1楼网友：鱼芗
- 2021-02-08 01:51
α∈(0,π/2)
α+π/6∈(π/6,2π/3)
cos(α+π/6)=4/5>0
∴α+π/6∈(π/6,π/2)
∴2α+π/3∈(π/3,π)
cos(2α+π/3)
=2cos²(α+π/6)-1
=2*(4/5)²-1
=32/25-1
=7/25>0
∴2α+π/3∈(π/3,π/2)
sin(2α+π/3)=24/25
sin(2α+π/12)
=sin(2α+π/3-π/4)
=sin(2α+π/3)cosπ/4-cos(2α+π/3)sinπ/4
=24/25*√2/2-7/25*√2/2
=24√2/50-7√2/50
=17√2/50希望能帮到你，祝学习进步，记得采纳，谢谢
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