高考问答类似烧错坟遇到鬼的文:请教高手一道简单的三角函数题～做对有加赏！！
来源：百度文库 编辑：高考问答 时间：2024/04/29 02:59:14
sina-sinb=1/3 cosa-cosb=1/2 求sin(a+b)
答案多少？怎么做的？
谢谢！
答案是 -12/13
答案多少？怎么做的？
谢谢！
答案是 -12/13
sin(a+b)=sinacosb+sinbcosa
(sina-sinb)(cosa-cosb)
=sinacosa-(sinacosb+sinbcosa)+sinbcosb
=1/2sin方a+1/2cos方b-(sinacosb+sinbcosa)
=1/2(sin方a+cos方b)-(sinacosb+sinbcosa)
=1/2-(sinacosb+sinbcosa)=1/6
所以sin(a+b)=1/3
sina-sinb=1/3 cosa-cosb=1/2
两边同时平方得：
(sina-sinb)^2=1/9 (cosa-cosb)^2=1/4
sin^a-2sina*sinb+sin^b=1/9
cos^a-2cosa*cosb+cos^b=1/4
(sin^a+sin^b+1/9)/2=sina*sinb
(cos^a+cos^b+1/4)/2=cosa*cosb
sin(a+b)=sinasinb+cosacosb
=(sin^a+sin^b+1/9)/2+(cos^a+cos^b+1/4)/2
=(sin^a+sin^b+1/9+cos^a+cos^b+1/4)/2
=(sin^a+sin^a+1/9+cos^b+cos^b+1/4)/2
=(2+1/9+1/4)/2
=(72+9+4)/72
=85/72