Let y = sin20sin40sin60sin80
a)show that y= (開方3)/2cos10cos50cos70
B) show that ysin10=3/16cos80
C) hence show that sin20sin40sin60sin80=3/16
TRIGONOMETRY M2
2011-03-15 2:55 am
回答 (1)
2011-03-15 3:45 am
✔ 最佳答案
(a) Consider ycos10cos50cos70= sin20sin40sin60sin80cos10cos50cos70
= cos70cos50(√3/2)cos10cos10cos50cos70
= (√3/2)(cos10cos50cos70)^2
So, y = (√3/2)cos10cos50cos70
(b) Consider ysin10/cos80
= (√3/2)[cos10cos50cos70sin10/cos80]
= (√3/4)[sin20cos50cos70/cos80]
= (√3/8)[(sin70 - sin30)cos70/cos80]
= (√3/16)[(sin140 - cos70)/cos80]
= (√3/16)[(cos50 - cos70)/cos80]
= (√3/16)[-2sin60sin(-10)/cos80]
= 3/16
So, ysin10 = (3/16)cos80
(c) y = (3/16)(cos80/sin10) = 3/16
= sin20sin40sin60sin80
=
收錄日期: 2021-04-26 14:43:57
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