若cos(x+y)cosy+sin(x+y)siny=0,则cosx=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 16:28:17
若cos(x+y)cosy+sin(x+y)siny=0,则cosx=若cos(x+y)cosy+sin(x+y)siny=0,则cosx=若cos(x+y)cosy+sin(x+y)siny=0,则

若cos(x+y)cosy+sin(x+y)siny=0,则cosx=
若cos(x+y)cosy+sin(x+y)siny=0,则cosx=

若cos(x+y)cosy+sin(x+y)siny=0,则cosx=
∵cos(x+y)cosy+sin(x+y)siny=0
==>cos[(x+y)-y]=0 (应用余弦差角公式cos(A-B)=cosAcosB+sinAsinB)
==>cosx=0
∴cosx=0.

根据公式cos(α-β)= cosαcosβ+sinαsinβ
原式 = cos(x+y-y) = cosx = 0