1) 2 sin^2(5/2)-1
2) sin^2 15° - sin^2 75°
3) if sinA = 1/3 and A is a acute, find the value of (cos A + cos2A)/(1+sinA+sin2A)
有a.maths 唔識做
2008-05-28 3:38 am
回答 (2)
2008-05-28 6:00 am
✔ 最佳答案
Q.1 Sorry, don't understand.Q.2 sin^2 15 - sin^2 75 = cos^2(90-15) - sin^2 75 = cos^2 75 - sin^2 75 = cos150=-cos30 = -sqrt3/2.
Q.3
Since sin A=1/3, therefore, cos A=(sqrt8)/3. sin2A = 2cosAsinA=(2)(sqrt8/3)(1/3)=
2sqrt8/9. cos2A = 1-2sin^2A = 1-2/9=7/9.
Therefore, (cosA + cos2A)/(1 + sinA + sin2A) = ( sqrt8/3 + 7/9)/( 1 + 1/3 + 2sqrt8/9) = (3sqrt8 + 7)/(9 + 3 + 2sqrt8) = (7 + 3sqrt8)/(12 + 2sqrt8).
2008-05-27 22:04:24 補充：
( 7 + 3sqrt8)/(12 + 2sqrt8) = (18 +11sqrt8)/56.
2008-06-18 1:54 am
2 sin^2(5/2)-1
= -cos (5)
= -cos (5)
收錄日期: 2021-04-25 22:36:11
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080527000051KK02312