已知1+cosA-sinB+sinAsinB=0.1-cosA-cosB+sinAscosB=0求sinA

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已知1+cosA-sinB+sinAsinB=0.1-cosA-cosB+sinAscosB=0求sinA
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已知1+cosA-sinB+sinAsinB=0.1-cosA-cosB+sinAscosB=0求sinA
已知1+cosA-sinB+sinAsinB=0.1-cosA-cosB+sinAscosB=0求sinA

已知1+cosA-sinB+sinAsinB=0.1-cosA-cosB+sinAscosB=0求sinA
1+cosa-sinb+sinasinb=0
1+cosa=sinb-sinasinb=sinb(1-sina).(1)
1-cosa-cosb+sinacosb=0
1-cosa=cosb-sinacosb=cosb(1-sina).(2)
(1)^2+(2)^2
(1-cosa)^2+(1+cosa)^2=(1-sina)^2
2+2cos^2a=1-2sina+sin^2a
4-2sin^2a=1-2sina+sin^2a
3sin^2a-2sina-3=0,
sina=(1+根号10)/3>1,舍去
或sina=(1-根号10)/3
故sina=(1-根号10)/3