已知π/2＜β＜α＜3π/4,且cos( α-β)=12/13, sin(α+β)=-3/5，求sin2α的值

王振安徽省 宿州市2017/7/26 8:43:14

已知π/2<y<x<3π/4,且cos(x-y)=12/13sin(x+y)=-3/5,求sin2x的值
解析：
因为π/2<y<x<3π/4
0<x-y<π/2
cos(x-y)=12/13
因为sin^(x-y)+cos^(x-y)=1
sin(x-y)>0
所以sin(x-y)=5/13
π<x+y<3π/2
所以cos(x+y)<0
sin(x+y)=-3/5,cos(x+y)=-4/5
sin2x=sin(x-y+x+y)=sin(x-y)cos(x+y)+cos(x-y)sin(x+y)
=(5/13)*(-4/5)+(12/13)*(-3/5)
=-59/65