设x=cosA/sinB,则x+1/x=2,化为x^2-2x+1=0,(x-1)^2=0,解得x=1,即cosA/sinB=1,cosB/sinA=1
cosA/sinB=sinA/cosB=1
cosA/sinA=sinB/cosB
cosAcosB=sinAsinB
cosAcosB-sinAsinB=0
cos(A+B)=0
A,B是锐角
A+B=90°
设x=cosA/sinB,则x+1/x=2,化为x^2-2x+1=0,(x-1)^2=0,解得x=1,即cosA/sinB=1,cosB/sinA=1
cosA/sinB=sinA/cosB=1
cosA/sinA=sinB/cosB
cosAcosB=sinAsinB
cosAcosB-sinAsinB=0
cos(A+B)=0
A,B是锐角
A+B=90°