Question

在△ABC中，已知，，求的值．

Answer 1

sinB=

在△ABC中，cosA=，∴sinA=．又sin(B－A)=，∴ 0＜B－A＜π．
∴cos(B－A)=，或cos(B－A)=．……6分若cos(B－A)=，則sinB=sin[A+(B－A)]
=sinAcos(B－A)+cosAsin(B－A)．…12分若cos(B－A)=，
則sinB=sin[A+(B－A)]=sinAcos(B－A)+cosAsin(B－A)（舍去）．
綜上所述，得sinB=