已知A,B满足1+cosA-sinB+sinAsinB=0,1-cosA-cosB+sinAsinB=0,则sinA的值?

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已知A,B满足1+cosA-sinB+sinAsinB=0,1-cosA-cosB+sinAsinB=0,则sinA的值?
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已知A,B满足1+cosA-sinB+sinAsinB=0,1-cosA-cosB+sinAsinB=0,则sinA的值?
已知A,B满足1+cosA-sinB+sinAsinB=0,1-cosA-cosB+sinAsinB=0,则sinA的值?

已知A,B满足1+cosA-sinB+sinAsinB=0,1-cosA-cosB+sinAsinB=0,则sinA的值?
由1+cosA-sinB+sinAsinB=0
得sinB= (1+cosA)/(1-sinA) (1)
由1-cosA-cosB+sinAcosB=0
得cosB= (1-cosA)/(1-sinA) (2)
(1)^2+(2)^2 得(1+cosA)^2+(1-cosA)^2=(1-sinA)^2
sinA=(1-√10)/3

1+cosA-sinB+sinAsinB=0(1)1-cosA-cosB+sinAcosB=0 (2)
(1) 得sinB= (1+cosA)/(1-sinA)
(2)得cosB= (1-cosA)/(1-sinA)
sin^2B+cos^2B=1
(1+cosA)/(1-sinA)^2+(1-cosA)/(1-sinA)^2=1
sinA=(1+-根号10)/3

很佩服一楼。。。。