已知sin(α-β)=36/85,cosβ=4/5（其中α、β均为锐角）
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解决时间 2021-03-03 22:53
- 提问者网友：遁入空寂
- 2021-03-03 06:42
已知sin(α-β)=36/85,cosβ=4/5（其中α、β均为锐角）
最佳答案
- 五星知识达人网友：零点过十分
- 2021-03-03 07:44
α、β为锐角
0-β<α-β<α-0
-90 < α-β < 90
所以cos(α-β) >0, sinβ>0
cos(α-β) = √(1- 36²/85²)=77/85
sinβ=√(1-4²/5²) = 3/5
sina = sin(a-b +b) = sin(a-b)cosb +cos(a-b)sinb = 36/85 * 4/5 + 77/85* 3/5 = 15/17
cosa = √(1-15²/17²)= 8/17
cosa = 2cos²a/2 -1
cos²a/2 =(8/17 +1)/2 = 25/34
sin²a/2 = 9/34
sina/2 = 3/√34
cosa/2 = 5/√34
tana/2 = 3/5
tan(a/2 +π/4) = (tana/2 +tanπ/4)/(1- tana/2 tan(π/4))
= (3/5 +1)/ (1-3/5)
=4
0-β<α-β<α-0
-90 < α-β < 90
所以cos(α-β) >0, sinβ>0
cos(α-β) = √(1- 36²/85²)=77/85
sinβ=√(1-4²/5²) = 3/5
sina = sin(a-b +b) = sin(a-b)cosb +cos(a-b)sinb = 36/85 * 4/5 + 77/85* 3/5 = 15/17
cosa = √(1-15²/17²)= 8/17
cosa = 2cos²a/2 -1
cos²a/2 =(8/17 +1)/2 = 25/34
sin²a/2 = 9/34
sina/2 = 3/√34
cosa/2 = 5/√34
tana/2 = 3/5
tan(a/2 +π/4) = (tana/2 +tanπ/4)/(1- tana/2 tan(π/4))
= (3/5 +1)/ (1-3/5)
=4
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