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一道三角函数题请求帮助,谢谢!
1已知sinx+siny=3/5,cosx+siny=4/5,且0<y<π.0<x<π求满足条件的x+y的所有取值....
1已知sinx+siny=3/5,cosx+siny=4/5,且0<y<π.0<x<π求满足条件的x+y的所有取值.
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sinx+cosy=3/5,cosx+siny=4/5
(sinx+cosy)2=9/25, ①
(cosx+siny)2=16/25,②
① + ②(即左右分别相加)得到
2+2(sinxcosy +cosxcosy)=1
sinxcosy +cosxcosy=-1/2
sin(x+y)=-1/2
x+y= 7π/6 or 11π/6
(sinx+cosy)2=9/25, ①
(cosx+siny)2=16/25,②
① + ②(即左右分别相加)得到
2+2(sinxcosy +cosxcosy)=1
sinxcosy +cosxcosy=-1/2
sin(x+y)=-1/2
x+y= 7π/6 or 11π/6
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