已知sin(α-β)cosα-cos(β-α)sinα=3/5,β是第三象限角,求sin(β+5π/4)的值

sin(α-β)cosα-cos(β-α)sinα=sin(α-β-a)=-sin(β)=3/5
=>sinβ=-3/5 cosβ=-4/5
sin(β+5π/4)=-sin(β+π/4)=-1/2*根号2 *(sinβ+cosβ)=7根号2/10