已知0＜β＜π/4,π/4＜α＜3π/4,cos(π/4-α)=3/5,sin(3π/4-β)=5/13,求cos(α+β)的值

题目

已知0＜β＜π/4,π/4＜α＜3π/4,cos(π/4-α)=3/5,sin(3π/4-β)=5/13,求cos(α+β)的值
答案是-56/65【要过程】

答案

π/4＜α＜3π/4,-π/2＜π/4-α＜0cos(π/4-α)=3/5sin(π/4-α)=-4/50＜β＜π/4π/2＜3π/4-β＜3π/4sin(3π/4-β)=5/13cos(3π/4-β)=-12/13cos(α+β)=-cos[π-(α+β)]=-cos[(π/4-α)+(3π/4-β)]=-[cos[(π...