已知锐角A,B满足(cosA/sinB)+(cosB/sinA)=2,求证A+B=90度
问题描述：
已知锐角A,B满足(cosA/sinB)+(cosB/sinA)=2,求证A+B=90度
答
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=1cosA/sinB=sinA/cosB=1cosA/sinA=sinB/cosBcosAcosB=sinAsinBcosAcosB-sinAsinB=0cos(A+B)=0A,B是锐角A+B=90°