1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值

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1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值

1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值

1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
sin(a-b)cosa-cos(b-a)sina=sin(a-b-a)=sin(-b)=-sin(b)=3/5;
sin(b)=-3/5;b是第三象限角,cos(b)=-4/5;
sin(b+5pi/4)=-sin(b+pi/4)=-sqrt(2)/2*(sin(b)+cos(b))=7*sqrt(2)/10
sqrt表示根号

因为cos(b-a)=cos(a-b)
所以
sin(a-b)cosa-cos(b-a)sina
=sin(a-b)cosa-cos(a-b)sina
=sin(a-b-a)
=sin(-b)
sinb
=-3/5
因为b是第三象限角,所以cosb=-4/5
sin(b+5pi/4)
=sin(b+pi/4+pi)

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因为cos(b-a)=cos(a-b)
所以
sin(a-b)cosa-cos(b-a)sina
=sin(a-b)cosa-cos(a-b)sina
=sin(a-b-a)
=sin(-b)
sinb
=-3/5
因为b是第三象限角,所以cosb=-4/5
sin(b+5pi/4)
=sin(b+pi/4+pi)
=-sin(pi/4+b)
=-(sin pi/4 * cosb+ cos pi/4 * sinb)
=(√2)/2 * 7/5
=10 分之 7*√2

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