设cos(A-B/2)=-1/9sin(A/2-B)=2/3A在90度到180度的开区间B在0到90度的开区间求cos(A+B)/2

Question

设cos(A-B/2)=-1/9 sin(A/2 -B)=2/3 A在90度到180度的开区间 B在0到90度的开区间 求cos(A+B)/2

Answer 1

A在90度到180度的开区间 B在0到90度的开区间
则A-B/2在45到180度之间,sin(A-B/2)为正的,由cos(A-B/2)=-1/9知道：sin
(A-B/2)=4√5/9,同理cos(A/2 -B)=√5/3
cos(A+B)/2
=cos[(A-B/2)-(A/2 -B)]
=cos(A-B/2)cos(A/2 -B)+sin(A-B/2)sin(A/2 -B)
=7√5/27