Question

若π/4＜α＜3π/4,0＜β＜π/4，cos(π/4-α)=3/5，sin（3π/4+β）=5/13，则sin(α+β)=？

这道题目我会做，但是算出来的答案就是跟标答不一样，所以要具体步骤和计算结果。

Answer 1

∵π/4＜α＜3π/4
∴-π/2<π/4-α<0
∵cos(π/4-α)=3/5
∴sin(π/4-α)=-4/5
∵0＜β＜π/4
∴3π/4<3π/4+β<π
∵sin（3π/4+β）=5/13
∴cos(3π/4+β)=-12/13
∴sin(α+β)=-cos(π/2+α+β)
=-cos[(3π/4+β)-(π/4-α)]
=-cos(3π/4+β)cos(π/4-α)- sin(3π/4+β)sin(π/4-α)
=12/13*3/5-5/13*(-4/5)
=56/65