已知0＜β＜π/4＜α＜3π/4,cos(π/4+α)=3/5,sina(3π/4+β)=5/13,求sina(2α+2β)的值已知0＜β＜π/4＜α＜3π/4,cos(π/4-α)=3/5,sina(3π/4+β)=5/13,求sina(α+β)的值
问题描述：
已知0＜β＜π/4＜α＜3π/4,cos(π/4+α)=3/5,sina(3π/4+β)=5/13,求sina(2α+2β)的值
已知0＜β＜π/4＜α＜3π/4,cos(π/4-α)=3/5,sina(3π/4+β)=5/13,求sina(α+β)的值
答
-π/2＜π/4-α＜0 -π＜π/2-2α＜0
3π/4＜3π/4+β＜π 3π/2＜3π/2+2β＜2π
cos(π/4+α)=3/5 sin(π/4+α)=-4/5 sin(π/2+2α)=-24/25
cos(π/2+2α)=1/25
sin(3π/4+β)=5/13 cos(3π/4+β)=-12/13 sin(3π/2+2β)=-120/169
cos(3π/2+2β)=49/169
sin(2α+2β)= sin(π/2+2α)cos(3π/2+2β)+sin(3π/2+2β)cos(π/2+2α)
答
cos(π/4-α)=3/5
π/4