Prove it hold for A+B+C = 180
cos^2 A + cos^2 B + cos^2 C - 1 = -2cosAcosBcosC
Math---module2 (F.4)
2010-02-25 4:32 am
回答 (1)
2010-02-25 5:50 am
✔ 最佳答案
cos^2 A + cos^2 B + cos^2 C - 1 = -2cosAcosBcosC LHS=cos^2 A + cos^2 B + cos^2 C - 1
= (cos2A +1)/2 + (cos2B +1)/2 + (cos2C +1)/2 - 1
= [cos2A + cos2B]/2 + cos(360-2A-2B)/2 + 1/2
= cos(A+B)cos(A-B) + cos(2A+2B)/2 + 1/2
= cos(A+B)cos(A-B) + cos^2(A+B)
= cos(A+B)[cos(A-B) + cos(A+B)]
= cos(180-C)[2cosAcosB]
= -2cosAcosBcosC
= RHS
收錄日期: 2021-04-13 17:06:34
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100224000051KK01416