Question

在三角形ABC中内角ABC的对边为abc已知cosA=2/3sinB=根号5cosC 求tanC的ŀ

Answer 1

∵cosA=2/3,
∴sinA=√(1-cos^2A)=√5/3
∵sinB=√辩念5cosC
sinB=sin(A+C)=sinAcosC+cosAsinC
∴sinAcosC+cosAsinC
=√5cosC
∴√迟灶宽码亮5/3cosC+2/3sinC
=√5cosC
sinC=√5cosC ,
∴tanC=√5

Answer 2

∵cosA=2/3,∴sinA=√(1-cos�0�5A)=√5/3
∵如培sinB=√5cosC
sinB=sin(A+C)=sinAcosC+cosAsinC
∴sinAcosC+cosAsinC=√5cosC
∴√灶带5/3cosC+2/隐橡芦3sinC=√5cosC
∴ sinC=√5cosC ,∴tanC=√5