cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求cos(A+B)的值.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/18 10:04:39
cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求cos(A+B)的值.cos(A-B/2)=-1/9,sin(A/2-B)=2/3

cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求cos(A+B)的值.
cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求cos(A+B)的值.

cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求cos(A+B)的值.
cos[(a+b)/2]= cos[(2a-b)/2-(a-2b)/2] =cos[(2a-b)/2]cos[(a-2b)/2]+sin[(2a-b)/2]sin[(a-2b)/2]
cos[a-(b/2)]=-1/9 -> sin[a-(b/2)]=4根号5/9
sin[(a/2)-b]=2/3 -> cos[(a/2)-b]=根号5/3
cos((a+b)/2)=7根号5/27
cos(a+b)=2cos^2((a+b)/2)-1
=2*(7根号5/27)^2-1
=2*245/729-1
=-239/729