若2sinx+3cosy=1,2cosx+3siny=2,则sin(x+y)=?

问题描述:

若2sinx+3cosy=1,2cosx+3siny=2,则sin(x+y)=?

2sinx+3cosy=1(1)
,2cosx+3siny=2 (2)
(1)两边平方+(2)两边平方得
4sin²x+12sinxcosy+9cos²y+4cos²x+12cosxsiny+9sin²y=5
12(sinxcosy+cosxsiny)=-8
12sin(x+y)=-8
sin(x+y)=-2/3