f(x)=sinxcosa+cosxsina=sin(x+a),f(π)=sin(π+a)=-sina=-1,因为0f(C)=sin(C+π/2)=cos(C)=1/2,所以C=π/3,又由sinB=2sinA=2sin(2π/3-B)=(根3)cosB+sinB,所以cosB=0,所以B=π/2,所以A=π/6.
证毕