cos(x-y⼀2)=-1⼀9,sin(x⼀2-y)=2⼀3,π⼀2<x<π,0<y<π⼀2 求cos((x+y)⼀2)的值

2025-05-09 04:00:50
推荐回答(1个)
回答1:

因为π/2
所以-π/2<-y<0

-π/4<-y/2<0,π/4
所以π/4
根据题目中所给的数,可以所小范围

π/2
所以sin(x-y/2)=4根号5/9

cos(x/2-y)=根号5/3

所以cos[(x+y)/2]=cos[(x-y/2)-(x/2-y)]=cos(x-y/2)cos(x/2-y)+sin(x-y/2)sin(x/2-y)=7根号5/27