已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?

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已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?

已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?

已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
cos(x-y)=cosxcosy-sinxsiny sin(x+y)=sinxcosy+cosxsiny
上式左边=(cosx)^2cosy-sinxcosxsiny+(sinx)^2cosy+sinxcosxsiny
=cosy=m
所以,siny=+-(1-m^2)^(1/2) 因为y为第三象限角,所以siny为负
所以,siny=-(1-m^2)^(1/2)